From a045600acb1d6e61e4978d1879ec3f07081a5ce0 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 29 Nov 2023 21:16:13 +0000 Subject: [PATCH] build based on 5379f0d --- stable | 2 +- v0.3 | 1 + v0.3.2/.documenter-siteinfo.json | 1 + v0.3.2/assets/documenter.js | 889 ++++++++++++++++++++++ v0.3.2/assets/themes/documenter-dark.css | 7 + v0.3.2/assets/themes/documenter-light.css | 9 + v0.3.2/assets/themeswap.js | 84 ++ v0.3.2/assets/warner.js | 52 ++ v0.3.2/exactranktest/index.html | 7 + v0.3.2/example/index.html | 153 ++++ v0.3.2/general/index.html | 2 + v0.3.2/index.html | 2 + v0.3.2/rankplot.svg | 206 +++++ v0.3.2/ranksim/index.html | 8 + v0.3.2/search_index.js | 3 + v0.3.2/siteinfo.js | 1 + v0.3.2/twosampletest/index.html | 13 + versions.js | 3 +- 18 files changed, 1441 insertions(+), 2 deletions(-) create mode 120000 v0.3 create mode 100644 v0.3.2/.documenter-siteinfo.json create mode 100644 v0.3.2/assets/documenter.js create mode 100644 v0.3.2/assets/themes/documenter-dark.css create mode 100644 v0.3.2/assets/themes/documenter-light.css create mode 100644 v0.3.2/assets/themeswap.js create mode 100644 v0.3.2/assets/warner.js create mode 100644 v0.3.2/exactranktest/index.html create mode 100644 v0.3.2/example/index.html create mode 100644 v0.3.2/general/index.html create mode 100644 v0.3.2/index.html create mode 100644 v0.3.2/rankplot.svg create mode 100644 v0.3.2/ranksim/index.html create mode 100644 v0.3.2/search_index.js create mode 100644 v0.3.2/siteinfo.js create mode 100644 v0.3.2/twosampletest/index.html diff --git a/stable b/stable index 610220f..3e13853 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v0.1.6 \ No newline at end of file +v0.3.2 \ No newline at end of file diff --git a/v0.3 b/v0.3 new file mode 120000 index 0000000..3e13853 --- /dev/null +++ b/v0.3 @@ -0,0 +1 @@ +v0.3.2 \ No newline at end of file diff --git a/v0.3.2/.documenter-siteinfo.json b/v0.3.2/.documenter-siteinfo.json new file mode 100644 index 0000000..53cbdf6 --- /dev/null +++ b/v0.3.2/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2023-11-29T21:16:09","documenter_version":"1.2.0"}} \ No newline at end of file diff --git a/v0.3.2/assets/documenter.js b/v0.3.2/assets/documenter.js new file mode 100644 index 0000000..f531160 --- /dev/null +++ b/v0.3.2/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.3.2/assets/themes/documenter-dark.css b/v0.3.2/assets/themes/documenter-dark.css new file mode 100644 index 0000000..9f5449f --- /dev/null +++ b/v0.3.2/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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span{font-style:inherit;font-weight:inherit}html.theme--documenter-dark strong{color:#f2f2f2;font-weight:700}html.theme--documenter-dark fieldset{border:none}html.theme--documenter-dark pre{-webkit-overflow-scrolling:touch;background-color:#282f2f;color:#fff;font-size:.875em;overflow-x:auto;padding:1.25rem 1.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark pre code{background-color:transparent;color:currentColor;font-size:1em;padding:0}html.theme--documenter-dark table td,html.theme--documenter-dark table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:inherit}html.theme--documenter-dark table th{color:#f2f2f2}html.theme--documenter-dark .box{background-color:#343c3d;border-radius:8px;box-shadow:none;color:#fff;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 0.5em 1em -0.125em rgba(10,10,10,0.1),0 0 0 1px 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.button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark 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.button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v0.3.2/assets/themeswap.js b/v0.3.2/assets/themeswap.js new file mode 100644 index 0000000..9f5eebe --- /dev/null +++ b/v0.3.2/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v0.3.2/assets/warner.js b/v0.3.2/assets/warner.js new file mode 100644 index 0000000..3f6f5d0 --- /dev/null +++ b/v0.3.2/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v0.3.2/exactranktest/index.html b/v0.3.2/exactranktest/index.html new file mode 100644 index 0000000..dd44ab2 --- /dev/null +++ b/v0.3.2/exactranktest/index.html @@ -0,0 +1,7 @@ + +Exact Rank Tests · MCMCTesting.jl

Exact Rank Hypothesis Tests

Introduction

The exact rank hypothesis testing strategy is based on Algorithm 2 by Gandy & Scott (2021)[GS2021].

ExactRankTest

The ranks are computed by simulating a single Markov chain backwards and forward. First, a random midpoint is simulated as

\[\begin{aligned} + M \sim \mathrm{Uniform}(1,\;L), +\end{aligned}\]

where $L = \texttt{n\_mcmc\_steps}$. Then, we simulate the Markov chain forward and backward as

\[\begin{alignat*}{3} + \theta_{M-l} &\sim K\left(\theta_{L-l+1}, \cdot \right) \qquad &&\text{for}\; l = 1, \ldots, M-1 \\ + \theta_{l} &\sim K\left(\theta_{l-1}, \cdot \right) \qquad &&\text{for}\; l = M+1, \ldots, L +\end{alignat*}\]

forming the chain

\[\theta_1,\; \ldots, \; \theta_{M},\; \ldots, \; \theta_{L}.\]

The rank is the ranking of the statistics of $\theta_{M}$. If the sampler and the model are correct, the rank has an uniform distribution as long as the midpoint is independently sampled.

MCMCTesting.ExactRankTest — Type
ExactRankTest(n_samples, n_mcmc_steps; n_mcmc_thin)

Exact rank hypothesis testing strategy for reversible MCMC kernels. Algorithm 2 in Gandy & Scott (2021).

Arguments

  • n_samples::Int: Number of ranks to be simulated.
  • n_mcmc_steps::Int: Number of MCMC states to be simulated for simulating a single rank.
  • n_mcmc_thin::Int: Number of thinning applied to the MCMC chain.

Returns

  • pvalues: P-value computed for each dimension of the statistic returned from statistics.

Requirements

This test requires the following functions for model and kernel to be implemented:

  • markovchain_transition
  • sample_joint

Furthermore, this test explicitly assumes the following

  • kernel is reversible.

Applying this tests to an irreversible kernel will result in false negatives even if its stationary distribution is correct.

Keyword Arguments for Tests

When calling mcmctest or seqmcmctest, this tests has an additional keyword argument:

  • uniformity_test_pvalue: The p-value calculation strategy.

The default strategy is an $\chi^2$ test. Any function returning a single p-value from a uniformity hypothesis test will work. The format is as follows:

uniformity_test_pvalue(x::AbstractVector)::Real
source

References

  • GS2021Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.
diff --git a/v0.3.2/example/index.html b/v0.3.2/example/index.html new file mode 100644 index 0000000..6d03ade --- /dev/null +++ b/v0.3.2/example/index.html @@ -0,0 +1,153 @@ + +Tutorial · MCMCTesting.jl

Tutorial

Problem Setup

Let's consider a simple Normal-Normal model:

\[\begin{aligned} +\theta_1 &\sim \mathrm{normal}\left(0, \sigma^2\right) \\ +\theta_2 &\sim \mathrm{normal}\left(0, \sigma^2\right) \\ +y &\sim \mathrm{normal}\left(\theta_1 + \theta_2, \sigma_{\epsilon}^2\right). +\end{aligned}\]

The joint log-likelihood can be implemented as follows:

using Random
+using Distributions
+
+struct Model
+    sigma    ::Float64
+    sigma_eps::Float64
+    y        ::Float64
+end
+nothing

For sampling from the posterior, a simple Gibbs sampling strategy is possible:

struct Gibbs end
+
+function complete_conditional(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)
+    μ = σ²/(σ²_ϵ + σ²)*(y - θ)
+    σ = 1/sqrt(1/σ²_ϵ + 1/σ²)
+    Normal(μ, σ)
+end
+
+function step(rng::Random.AbstractRNG, model::Model, ::Gibbs, θ)
+    θ    = copy(θ)
+    y    = model.y
+    σ²   = model.sigma^2
+    σ²_ϵ = model.sigma_eps^2
+    θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))
+    θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))
+    θ
+end
+nothing

Testing the Gibbs Sampler

All of the functionalities of MCMCTesting assume that we can sample from the joint distribution $p(\theta, y)$. This is done by as follows:

using MCMCTesting
+
+function MCMCTesting.sample_joint(rng::Random.AbstractRNG, model::Model)
+    θ₁ = rand(rng, Normal(0, model.sigma))
+    θ₂ = rand(rng, Normal(0, model.sigma))
+    θ  = [θ₁, θ₂]
+    y  = rand(rng, Normal(θ[1] + θ[2], model.sigma_eps))
+    θ, y
+end
+nothing

The Gibbs samplers can be connected to MCMCTesting by implementing the following:

using Accessors
+
+function MCMCTesting.markovchain_transition(
+    rng::Random.AbstractRNG, model::Model, kernel, θ, y
+)
+    model′ = @set model.y = only(y)
+    step(rng, model′, kernel, θ)
+end
+nothing

Let's check that the implementation is correct by 

model = Model(1., .5, randn())
+kernel = Gibbs()
+test = TwoSampleTest(100, 100)
+subject = TestSubject(model, kernel)
+seqmcmctest(test, subject, 0.0001, 100; show_progress=false)
true

true means that the tests have passed.

Now, let's consider two erroneous implementations:

struct GibbsWrongMean end
+
+function complete_conditional_wrongmean(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)
+    μ = σ²/(σ²_ϵ + σ²)*(y + θ)
+    σ = 1/sqrt(1/σ²_ϵ + 1/σ²)
+    Normal(μ, σ)
+end
+
+function step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongMean, θ)
+    θ    = copy(θ)
+    y    = model.y
+    σ²   = model.sigma^2
+    σ²_ϵ = model.sigma_eps^2
+
+    θ[1] = rand(rng, complete_conditional_wrongmean(θ[2], σ², σ²_ϵ, y))
+    θ[2] = rand(rng, complete_conditional_wrongmean(θ[1], σ², σ²_ϵ, y))
+    θ
+end
+
+struct GibbsWrongVar end
+
+function complete_conditional_wrongvar(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)
+    μ = σ²/(σ²_ϵ + σ²)*(y - θ)
+    Normal(μ, sqrt(σ²))
+end
+
+function step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongVar, θ)
+    θ    = copy(θ)
+    y    = model.y
+    σ²   = model.sigma^2
+    σ²_ϵ = model.sigma_eps^2
+
+    if rand(Bernoulli(0.5))
+        θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))
+        θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))
+    else
+        θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))
+        θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))
+    end
+    θ
+end
+nothing

The kernel with a wrong mean fails:

kernel = GibbsWrongMean()
+subject = TestSubject(model, kernel)
+seqmcmctest(test, subject, 0.0001, 100; show_progress=false)
false

and so does the one with the wrong variance:

kernel = GibbsWrongVar()
+subject = TestSubject(model, kernel)
+seqmcmctest(test, subject, 0.0001, 100; show_progress=false)
false

Visualizing Simulated Ranks

MCMCTesting also provides some basic plot recipes for visualizing the simulated rank for the exact rank test. For this, Plots must be imported before MCMCTesting.

using Plots
+gr()
+using MCMCTesting
+nothing

Also, since the exact rank test explicitly requires the MCMC kernel to be reversible, we modify the previous Gibbs sampler to use a random scan order.

function step(rng::Random.AbstractRNG, model::Model, ::Gibbs, θ)
+    θ    = copy(θ)
+    y    = model.y
+    σ²   = model.sigma^2
+    σ²_ϵ = model.sigma_eps^2
+    if rand(Bernoulli(0.5))
+        θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))
+        θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))
+    else
+        θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))
+        θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))
+    end
+    θ
+end
+
+function step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongVar, θ)
+    θ    = copy(θ)
+    y    = model.y
+    σ²   = model.sigma^2
+    σ²_ϵ = model.sigma_eps^2
+    if rand(Bernoulli(0.5))
+        θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))
+        θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))
+    else
+        θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))
+        θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))
+    end
+    θ
+end
+nothing

Then, we can simulate the ranks and then plot them using Plots.

test = ExactRankTest(1000, 10, 10)
+
+rank_correct = simulate_ranks(test, TestSubject(model, Gibbs()); show_progress=false)
+rank_wrong = simulate_ranks(test, TestSubject(model, GibbsWrongVar()); show_progress=false)
+
+stat_names = ["θ1 mean correct", "θ2 mean correct", "θ1 var correct", "θ2 var correct"]
+rankplot(test, rank_correct; stat_names)
+
+stat_names = ["θ1 mean wrong", "θ2 mean wrong", "θ1 var wrong", "θ2 var wrong"]
+rankplot!(test, rank_wrong; stat_names)
+
+savefig("rankplot.svg")
+nothing
qt.qpa.xcb: could not connect to display
+qt.qpa.plugin: From 6.5.0, xcb-cursor0 or libxcb-cursor0 is needed to load the Qt xcb platform plugin.
+qt.qpa.plugin: Could not load the Qt platform plugin "xcb" in "" even though it was found.
+This application failed to start because no Qt platform plugin could be initialized. Reinstalling the application may fix this problem.
+
+Available platform plugins are: xcb, eglfs, minimal, vkkhrdisplay, offscreen, minimalegl, linuxfb, vnc.
+
+Aborted (core dumped)
+connect: Connection refused
+GKS: can't connect to GKS socket application
+
+GKS: Open failed in routine OPEN_WS
+GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

If the MCMC kernel under test is reversible and correct, the ranks must resemble samples from a uniform distribution. The colored bands around black line show the 1σ, 2σ, and 3σ deviations from the null hypothesis. Here, we can see that the ranks of the erroneous kernel are not uniform.

diff --git a/v0.3.2/general/index.html b/v0.3.2/general/index.html new file mode 100644 index 0000000..ac10ed2 --- /dev/null +++ b/v0.3.2/general/index.html @@ -0,0 +1,2 @@ + +General Usage · MCMCTesting.jl

General Usage

Introduction

The tests provided by MCMCTesting are frequentist hypothesis tests for testing the correctness of MCMC kernels. In particular, it compute the p-value for the null hypothesis that the MCMC kernel has the correct stationary distribution against the alternative hypothesis that it doesn't.

Currently, MCMCTesting provide three different tests originally proposed by Gandy and Scott[gandyandscott2021]:

  1. Simple Two-Sample Test
  2. Two-Sample Test with an Additional Gibbs Step
  3. Exact Rank Test

The two-sample tests are generally applicable. On the other hand, the exact rank test assumes that the MCMC kernel is reversible. Therefore, it can specifically be used to test reversibility.

Interface

The user needs to implement the following function specializations for the model and kernel subject to the test.

MCMCTesting.sample_joint — Function
sample_joint(rng, model)

Sample from the joint distribution of the prior and the predictive distribution of model.

Arguments

  • rng::Random.AbstractRNG: Random number generator.
  • model: Model subject to test.

Returns

  • θ: Model parameter sampled from the prior p(θ).
  • y: Data generated from conditionally on θ from p(y|θ)
source
MCMCTesting.markovchain_transition — Function
markovchain_transition(rng, model, kernel, θ, y)

Perform a single Markov chain transition of kernel on the previous state θ targeting the posterior of model conditioned on y.

Arguments

  • rng::Random.AbstractRNG: Random number generator.
  • model: Model forming the posterior p(θ|y) conditioned on y.
  • θ: Previous state of the Markov chain.
  • y: Data to condition on.

Returns

  • θ′: Next state of the Markov chain.
source

Some tests might be require additional interfaces to be implemented. For an overview of how to implement these interfaces, refer to the tutorial.

The model and kernel are then passed to MCMCTesting through the following struct:

MCMCTesting.TestSubject — Type
TestSubject(model, kernel)

Model and MCMC kernel obejct subject to test.

Arguments

  • model: Model subject to test.
  • kernel: MCMC kernel subject to test.
source

Simulating a P-Value with mcmctest

Each of the test internally run simulations and compute a single p-value through the following routine:

MCMCTesting.mcmctest — Function
mcmctest([rng,] test, subject; kwargs...)

Sample a p-value according to test for subject

Arguments

  • rng::Random.AbstractRNG: Random number generator. (Default: Random.default_rng().)
  • test::AbstractMCMCTest: Test strategy.
  • subject::TestSubject: MCMC algorithm and model subject to test.

Keyword Arguments

  • show_progress::Bool: Whether to show the progress bar. (Default: true.)
  • statistics: Function for computing test statistics from samples generated from the tests. (See section below for additional description.)
  • Check the documentation for the respective test strategy for additional keyword arugments.

Custom Test Statistics

The statistics used for the hypothesis tests can be modified by passing a custom funciton to statistics. The default statistics are the first and second moments computed as below.

statistics = params -> vcat(params, params.^2)

The cross-interaction can also be tested by adding an additional entry as below.

statistics = params -> vcat(params, params.^2, reshape(params*params',:))

But naturally, adding more statistics increase the computational cost of computing the tests.

Also, different tests may result in different statistics being computed through the same statistics function. For example, the two-sample test strategies generate both model parameters θ and data y. Therefore, params = vcat(θ, y). On the other hand, the exac rank test only generates model parameters θ. Therefore, params = θ. Naturally, statistics can also be used to select a subset of parameters used for testing. For example, for the two-sample test strategies, if we only want to use θ for the tests, where d = length(θ) > 0, one can do the following:

statistics = params -> θ[1:d]
source

Increasing Power with seqmcmctest

seqmcmctest (Algorithm 3[gandyandscott2021]) sequentially calls mcmctest to increase the power and ensure a low false rejection rate. Furthermore, the p-values from each component of the statistics are combined through multiple hypothesis adjustment.

MCMCTesting.seqmcmctest — Function
seqmcmctest([rng,] test, subject, false_rejection_rate, samplesize; kwargs...)

Sequential run multiple hypothesis tests to guarantee false_rejection_rate.

Arguments

  • rng::Random.AbstractRNG: Random number generator.
  • test::AbstractMCMCTest: Test strategy.
  • subject::TestSubject: MCMC algorithm and model subject to test.
  • false_rejection_rate::Real: Desired false rejection rate.
  • samplesize::Int: The number of p-values used at each test iteration.

Keyword Arguments

  • samplesize_increase: Factor of increase for the samplsize after the first test iteration turns out inconclusive. (Default: 2.0)
  • show_progress::Bool: Whether to show progress. (Default: true)
  • pvalue_adjustmeht::MultipleTesting.PValueAdjustment: P-value adjustment for multiple testing over the elements of the statistic. (Default: MultipleTesting.Bonferroni())

Additional keyword arguments are passed to internal calls to mcmctest.

Returns

  • test_result::Bool: true if the null-hypothesis (the MCMC algorithm has the correct stationary distribution) wasn't rejected, false otherwise.
source

References

  • gandyandscott2021Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.
diff --git a/v0.3.2/index.html b/v0.3.2/index.html new file mode 100644 index 0000000..5d95941 --- /dev/null +++ b/v0.3.2/index.html @@ -0,0 +1,2 @@ + +Home · MCMCTesting.jl

MCMCTesting

Documentation for MCMCTesting.

MCMCTesting provides the MCMC testing algorithms developed by Gandy & Scott (2021)[GS2021]. These tests can be seen as an improvement of the hypothesis testing approach proposed by Geweke [G2004]. Unlike simulation-based calibration (SBC; [TBSVG2018][YD2023][MMKBPBHFGV2022]), these tests are more appropriate for testing the exactness of the MCMC algorithm rather than the identifiability of the models. This is because the tests focus on maximizing the power for verify the validity of individual Markov transitions instead of a set of samples. Furthermore, unlike SBC, the approach of Gandy & Scott[GS2021] is able to exactly satisfy the assumptions required for the theoretical guarantees.

References

  • GS2021Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.
  • G2004Geweke, J. (2004). Getting it right: Joint distribution tests of posterior simulators. Journal of the American Statistical Association, 99(467), 799-804.
  • TBSVG2018Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2018). Validating Bayesian inference algorithms with simulation-based calibration. arXiv preprint arXiv:1804.06788.
  • YD2023Yao, Y., & Domke, J. (2023, November). Discriminative Calibration: Check Bayesian Computation from Simulations and Flexible Classifier. In Thirty-seventh Conference on Neural Information Processing Systems.
  • MMKBPBHFGV2022Modrák, M., Moon, A. H., Kim, S., Bürkner, P., Huurre, N., Faltejsková, K., ... & Vehtari, A. (2022). Simulation-based calibration checking for Bayesian computation: The choice of test quantities shapes sensitivity. arXiv preprint arXiv:2211.02383.
diff --git a/v0.3.2/rankplot.svg b/v0.3.2/rankplot.svg new file mode 100644 index 0000000..7c2cb5d --- /dev/null +++ b/v0.3.2/rankplot.svg @@ -0,0 +1,206 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.3.2/ranksim/index.html b/v0.3.2/ranksim/index.html new file mode 100644 index 0000000..a79bf89 --- /dev/null +++ b/v0.3.2/ranksim/index.html @@ -0,0 +1,8 @@ + +Visualizing Ranks · MCMCTesting.jl

Visualizing Ranks

Introduction

This section documents how to visualize ranks sampled using Algorithm 2 by Gandy & Scott (2021)[GS2021]. For more information, refer to the documentation for the exact rank test.

Simulating Ranks

MCMCTesting.simulate_ranks — Function
simulate_ranks([rng,] test, subject; kwargs...)

Simulate ranks according to the exact rank test strategy.

Arguments

  • rng::Random.AbstractRNG: Random number generator. (Default: Random.default_rng().)
  • test::AbstractMCMCTest: Test strategy.
  • subject::TestSubject: MCMC algorithm and model subject to test.

Keyword Arguments

  • tie_epsilon::Real: The tolerance for declaring a difference in statistic as a tie. (Default: eps(Float32).)
  • statistics: Function for computing test statistics from samples generated from the tests. (See section below for additional description.)
  • show_progress::Bool: Whether to show progress.

Returns

  • ranks::Matrix: The simualted ranks. Each row are the rank samples of each statistic.
source

Visualizing Ranks with Plots

We provide a Plots recipe for visualizing the ranks:

MCMCTesting.rankplot — Function
rankplot(test, ranks; kwargs...)

Plot the simulated ranks using simulate_ranks. If the test subjects are correct, the ranks should visually resemble samples from a uniform distribution. The black horizontal line shows the density of a uniform distribution, while the colored bands are the 1σ, 2σ, 3σ confidence intervals.

Info

The confidence intervals are derived from the normal approximation of binomials observations and assume uniformly-sized bins.

Info

Plots must be imported to use this plot recipe.

Arguments

  • test::ExactRankTest: The exact rank test object used to simulate the ranks.
  • ranks: The output of simulate_rank.

Keyword Arguments

  • stats_names: The name for the statistics used in the rank simulation. The default argument automatically assign default names. (Default: :auto).
  • Keyword arguments corresponding Plots attributes, such as bins, layout, size, may apply.
source

This can be used as follows:

using Plots
+using MCMCTesting
+
+# Set the simulation here
+
+ranks = simulate_ranks(test, subject)
+rankplot(test, ranks; param_names)

Also refer to the tutorial for a working example.

References

  • GS2021Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.
diff --git a/v0.3.2/search_index.js b/v0.3.2/search_index.js new file mode 100644 index 0000000..88ae34c --- /dev/null +++ b/v0.3.2/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"twosampletest/#Two-Sample-Hypothesis-Tests","page":"Two-Sample Tests","title":"Two Sample Hypothesis Tests","text":"","category":"section"},{"location":"twosampletest/#Introduction","page":"Two-Sample Tests","title":"Introduction","text":"","category":"section"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"The two-sample hypothesis testing strategies are based on Algorithm 1 by Gandy & Scott (2021)[gandyandscott2021].","category":"page"},{"location":"twosampletest/#twosample","page":"Two-Sample Tests","title":"TwoSampleTest","text":"","category":"section"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"The first basic strategy generates the treatment group","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"beginaligned\n theta y_texttrtm sim pleft(theta yright) \n theta_texttrtm sim Kleft(theta cdotright)\nendaligned","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"and the control group as","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"beginaligned\n theta_textctrl y_textctrl sim pleft(theta yright) \nendaligned","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"where the test compares ","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"(theta_texttrtm y_texttrtm)\nquadtextversusquad \n(theta_textctrl y_textctrl)","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"TwoSampleTest","category":"page"},{"location":"twosampletest/#MCMCTesting.TwoSampleTest","page":"Two-Sample Tests","title":"MCMCTesting.TwoSampleTest","text":"TwoSampleTest(n_samples, n_mcmc_steps; n_control, n_treatment, n_mcmc_thin)\n\nTwo-sample hypothesis testing strategy. Algorithm 1 in Gandy & Scott (2021).\n\nArguments\n\nn_samples::Int: Number of samples from the joint p(θ, y) used for the computing the p-values.\nn_mcmc_steps::Int: Number of times the MCMC kernel is applied to initial sample from the joint. (Increasing this value improves the power of the test.)\n\nKeyword Arguments\n\nn_control::Int: Number of pure samples from the joint (control group). (Default: n_samples)\nn_treatment::Int: Number of samples from the MCMC kernel (treatment group). (Default: n_samples)\nn_mcmc_thin::Int: Number of thinning applied to the MCMC chain. The effect of this argument is the same as n_mcmc_steps.\n\nReturns\n\npvalues: P-value computed for each dimension of the statistic returned from statistics.\n\nRequirements\n\nThis test requires the following functions for model and kernel to be implemented:\n\nmarkovchain_transition\nsample_joint\n\nKeyword Arguments for Tests\n\nWhen calling mcmctest or seqmcmctest, this tests has an additional keyword argument:\n\ntwo_sample_test_pvalue: The p-value calculation strategy.\n\nThe default strategy is an approximate two-sample Kolmogorov-Smirnov test. Any function returning a single p-value from a two-sample hypothesis test will work. The format is as follows:\n\ntwo_sample_test_pvalue(x::AbstractVector, y::AbstractVector)::Real\n\n\n\n\n\n","category":"type"},{"location":"twosampletest/#twosamplegibbs","page":"Two-Sample Tests","title":"TwoSampleGibbsTest","text":"","category":"section"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"The second strategy performs applies an additional Gibbs sampling step when generating the treatment group as","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"beginaligned\n theta y sim pleft(theta yright) \n theta_texttrtm sim Kleft(theta cdotright) \n y_texttrtm sim pleft(y mid theta_texttrtmright)\nendaligned","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"resulting in the treatment group ","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"(theta_texttrtm y_texttrtm)","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"The control group is generated the same as TwoSampleTest.","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"To use this test, the user needs to implement the following interface for simulating from the conditional likelihood.","category":"page"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"sample_predictive","category":"page"},{"location":"twosampletest/#MCMCTesting.sample_predictive","page":"Two-Sample Tests","title":"MCMCTesting.sample_predictive","text":"sample_predictive(rng, model, θ)\n\nSample from the predictive distribution of model conditionally on θ\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator.\nmodel: Model subject to test.\nθ: Model parameters to condition on.\n\nReturns\n\ny: Data generated from conditionally on θ from p(y|θ)\n\n\n\n\n\n","category":"function"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"TwoSampleGibbsTest","category":"page"},{"location":"twosampletest/#MCMCTesting.TwoSampleGibbsTest","page":"Two-Sample Tests","title":"MCMCTesting.TwoSampleGibbsTest","text":"TwoSampleTest(n_samples, n_mcmc_steps; n_control, n_treatment, n_mcmc_thin)\n\nTwo-sample hypothesis testing strategy with an additional Gibbs sampling step. Modified version of Algorithm 1 in Gandy & Scott 2021 for increased power.\n\nArguments\n\nn_samples::Int: Number of samples from the joint p(θ, y) used for the computing the p-values.\nn_mcmc_steps::Int: Number of times the MCMC kernel is applied to initial sample from the joint. (Increasing this value improves the power of the test.)\n\nKeyword Arguments\n\nn_control::Int: Number of pure samples from the joint (control group). (Default: n_samples)\nn_treatment::Int: Number of samples from the MCMC kernel (treatment group). (Default: n_samples)\nn_mcmc_thin::Int: Number of thinning applied to the MCMC chain. The effect of this argument is the same as n_mcmc_steps.\n\nReturns\n\npvalues: P-value computed for each dimension of the statistic returned from statistics.\n\nRequirements\n\nThis test requires the following functions for model and kernel to be implemented:\n\nmarkovchain_transition\nsample_joint\nsample_predictive\n\nKeyword Arguments for Tests\n\nWhen calling mcmctest or seqmcmctest, this tests has an additional keyword argument:\n\ntwo_sample_test_pvalue: The p-value calculation strategy.\n\nThe default strategy is an approximate two-sample Kolmogorov-Smirnov test. Any function returning a p-value to two sample groups will work. The format is as follows:\n\ntwo_sample_test_pvalue(x::AbstractVector, y::AbstractVector)::Real\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"twosampletest/#References","page":"Two-Sample Tests","title":"References","text":"","category":"section"},{"location":"twosampletest/","page":"Two-Sample Tests","title":"Two-Sample Tests","text":"[gandyandscott2021]: Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.","category":"page"},{"location":"general/#General-Usage","page":"General Usage","title":"General Usage","text":"","category":"section"},{"location":"general/#Introduction","page":"General Usage","title":"Introduction","text":"","category":"section"},{"location":"general/","page":"General Usage","title":"General Usage","text":"The tests provided by MCMCTesting are frequentist hypothesis tests for testing the correctness of MCMC kernels. In particular, it compute the p-value for the null hypothesis that the MCMC kernel has the correct stationary distribution against the alternative hypothesis that it doesn't.","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"Currently, MCMCTesting provide three different tests originally proposed by Gandy and Scott[gandyandscott2021]: ","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"Simple Two-Sample Test\nTwo-Sample Test with an Additional Gibbs Step\nExact Rank Test","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"The two-sample tests are generally applicable. On the other hand, the exact rank test assumes that the MCMC kernel is reversible. Therefore, it can specifically be used to test reversibility.","category":"page"},{"location":"general/#Interface","page":"General Usage","title":"Interface","text":"","category":"section"},{"location":"general/","page":"General Usage","title":"General Usage","text":"The user needs to implement the following function specializations for the model and kernel subject to the test.","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"sample_joint\nmarkovchain_transition","category":"page"},{"location":"general/#MCMCTesting.sample_joint","page":"General Usage","title":"MCMCTesting.sample_joint","text":"sample_joint(rng, model)\n\nSample from the joint distribution of the prior and the predictive distribution of model.\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator.\nmodel: Model subject to test.\n\nReturns\n\nθ: Model parameter sampled from the prior p(θ).\ny: Data generated from conditionally on θ from p(y|θ)\n\n\n\n\n\n","category":"function"},{"location":"general/#MCMCTesting.markovchain_transition","page":"General Usage","title":"MCMCTesting.markovchain_transition","text":"markovchain_transition(rng, model, kernel, θ, y)\n\nPerform a single Markov chain transition of kernel on the previous state θ targeting the posterior of model conditioned on y.\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator.\nmodel: Model forming the posterior p(θ|y) conditioned on y.\nθ: Previous state of the Markov chain.\ny: Data to condition on.\n\nReturns\n\nθ′: Next state of the Markov chain.\n\n\n\n\n\n","category":"function"},{"location":"general/","page":"General Usage","title":"General Usage","text":"Some tests might be require additional interfaces to be implemented. For an overview of how to implement these interfaces, refer to the tutorial.","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"The model and kernel are then passed to MCMCTesting through the following struct:","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"TestSubject","category":"page"},{"location":"general/#MCMCTesting.TestSubject","page":"General Usage","title":"MCMCTesting.TestSubject","text":"TestSubject(model, kernel)\n\nModel and MCMC kernel obejct subject to test.\n\nArguments\n\nmodel: Model subject to test.\nkernel: MCMC kernel subject to test.\n\n\n\n\n\n","category":"type"},{"location":"general/#Simulating-a-P-Value-with-mcmctest","page":"General Usage","title":"Simulating a P-Value with mcmctest","text":"","category":"section"},{"location":"general/","page":"General Usage","title":"General Usage","text":"Each of the test internally run simulations and compute a single p-value through the following routine:","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"mcmctest","category":"page"},{"location":"general/#MCMCTesting.mcmctest","page":"General Usage","title":"MCMCTesting.mcmctest","text":"mcmctest([rng,] test, subject; kwargs...)\n\nSample a p-value according to test for subject\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator. (Default: Random.default_rng().)\ntest::AbstractMCMCTest: Test strategy.\nsubject::TestSubject: MCMC algorithm and model subject to test.\n\nKeyword Arguments\n\nshow_progress::Bool: Whether to show the progress bar. (Default: true.)\nstatistics: Function for computing test statistics from samples generated from the tests. (See section below for additional description.)\nCheck the documentation for the respective test strategy for additional keyword arugments.\n\nCustom Test Statistics\n\nThe statistics used for the hypothesis tests can be modified by passing a custom funciton to statistics. The default statistics are the first and second moments computed as below.\n\nstatistics = params -> vcat(params, params.^2)\n\nThe cross-interaction can also be tested by adding an additional entry as below.\n\nstatistics = params -> vcat(params, params.^2, reshape(params*params',:))\n\nBut naturally, adding more statistics increase the computational cost of computing the tests.\n\nAlso, different tests may result in different statistics being computed through the same statistics function. For example, the two-sample test strategies generate both model parameters θ and data y. Therefore, params = vcat(θ, y). On the other hand, the exac rank test only generates model parameters θ. Therefore, params = θ. Naturally, statistics can also be used to select a subset of parameters used for testing. For example, for the two-sample test strategies, if we only want to use θ for the tests, where d = length(θ) > 0, one can do the following:\n\nstatistics = params -> θ[1:d]\n\n\n\n\n\n","category":"function"},{"location":"general/#Increasing-Power-with-seqmcmctest","page":"General Usage","title":"Increasing Power with seqmcmctest","text":"","category":"section"},{"location":"general/","page":"General Usage","title":"General Usage","text":"seqmcmctest (Algorithm 3[gandyandscott2021]) sequentially calls mcmctest to increase the power and ensure a low false rejection rate. Furthermore, the p-values from each component of the statistics are combined through multiple hypothesis adjustment.","category":"page"},{"location":"general/","page":"General Usage","title":"General Usage","text":"seqmcmctest","category":"page"},{"location":"general/#MCMCTesting.seqmcmctest","page":"General Usage","title":"MCMCTesting.seqmcmctest","text":"seqmcmctest([rng,] test, subject, false_rejection_rate, samplesize; kwargs...)\n\nSequential run multiple hypothesis tests to guarantee false_rejection_rate.\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator.\ntest::AbstractMCMCTest: Test strategy.\nsubject::TestSubject: MCMC algorithm and model subject to test.\nfalse_rejection_rate::Real: Desired false rejection rate.\nsamplesize::Int: The number of p-values used at each test iteration.\n\nKeyword Arguments\n\nsamplesize_increase: Factor of increase for the samplsize after the first test iteration turns out inconclusive. (Default: 2.0)\nshow_progress::Bool: Whether to show progress. (Default: true)\npvalue_adjustmeht::MultipleTesting.PValueAdjustment: P-value adjustment for multiple testing over the elements of the statistic. (Default: MultipleTesting.Bonferroni())\n\nAdditional keyword arguments are passed to internal calls to mcmctest.\n\nReturns\n\ntest_result::Bool: true if the null-hypothesis (the MCMC algorithm has the correct stationary distribution) wasn't rejected, false otherwise.\n\n\n\n\n\n","category":"function"},{"location":"general/#References","page":"General Usage","title":"References","text":"","category":"section"},{"location":"general/","page":"General Usage","title":"General Usage","text":"[gandyandscott2021]: Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.","category":"page"},{"location":"ranksim/#ranksim","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"","category":"section"},{"location":"ranksim/#Introduction","page":"Visualizing Ranks","title":"Introduction","text":"","category":"section"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"This section documents how to visualize ranks sampled using Algorithm 2 by Gandy & Scott (2021)[GS2021]. For more information, refer to the documentation for the exact rank test.","category":"page"},{"location":"ranksim/#Simulating-Ranks","page":"Visualizing Ranks","title":"Simulating Ranks","text":"","category":"section"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"simulate_ranks","category":"page"},{"location":"ranksim/#MCMCTesting.simulate_ranks","page":"Visualizing Ranks","title":"MCMCTesting.simulate_ranks","text":"simulate_ranks([rng,] test, subject; kwargs...)\n\nSimulate ranks according to the exact rank test strategy.\n\nArguments\n\nrng::Random.AbstractRNG: Random number generator. (Default: Random.default_rng().)\ntest::AbstractMCMCTest: Test strategy.\nsubject::TestSubject: MCMC algorithm and model subject to test.\n\nKeyword Arguments\n\ntie_epsilon::Real: The tolerance for declaring a difference in statistic as a tie. (Default: eps(Float32).)\nstatistics: Function for computing test statistics from samples generated from the tests. (See section below for additional description.)\nshow_progress::Bool: Whether to show progress.\n\nReturns\n\nranks::Matrix: The simualted ranks. Each row are the rank samples of each statistic.\n\n\n\n\n\n","category":"function"},{"location":"ranksim/#Visualizing-Ranks-with-Plots","page":"Visualizing Ranks","title":"Visualizing Ranks with Plots","text":"","category":"section"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"We provide a Plots recipe for visualizing the ranks:","category":"page"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"rankplot","category":"page"},{"location":"ranksim/#MCMCTesting.rankplot","page":"Visualizing Ranks","title":"MCMCTesting.rankplot","text":"rankplot(test, ranks; kwargs...)\n\nPlot the simulated ranks using simulate_ranks. If the test subjects are correct, the ranks should visually resemble samples from a uniform distribution. The black horizontal line shows the density of a uniform distribution, while the colored bands are the 1σ, 2σ, 3σ confidence intervals.\n\ninfo: Info\nThe confidence intervals are derived from the normal approximation of binomials observations and assume uniformly-sized bins.\n\ninfo: Info\nPlots must be imported to use this plot recipe.\n\nArguments\n\ntest::ExactRankTest: The exact rank test object used to simulate the ranks.\nranks: The output of simulate_rank.\n\nKeyword Arguments\n\nstats_names: The name for the statistics used in the rank simulation. The default argument automatically assign default names. (Default: :auto). \nKeyword arguments corresponding Plots attributes, such as bins, layout, size, may apply.\n\n\n\n\n\n","category":"function"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"This can be used as follows:","category":"page"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"using Plots\nusing MCMCTesting\n\n# Set the simulation here\n\nranks = simulate_ranks(test, subject)\nrankplot(test, ranks; param_names)","category":"page"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"Also refer to the tutorial for a working example.","category":"page"},{"location":"ranksim/#References","page":"Visualizing Ranks","title":"References","text":"","category":"section"},{"location":"ranksim/","page":"Visualizing Ranks","title":"Visualizing Ranks","text":"[GS2021]: Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.","category":"page"},{"location":"exactranktest/#exactrank","page":"Exact Rank Tests","title":"Exact Rank Hypothesis Tests","text":"","category":"section"},{"location":"exactranktest/#Introduction","page":"Exact Rank Tests","title":"Introduction","text":"","category":"section"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"The exact rank hypothesis testing strategy is based on Algorithm 2 by Gandy & Scott (2021)[GS2021].","category":"page"},{"location":"exactranktest/#ExactRankTest","page":"Exact Rank Tests","title":"ExactRankTest","text":"","category":"section"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"The ranks are computed by simulating a single Markov chain backwards and forward. First, a random midpoint is simulated as","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"beginaligned\n M sim mathrmUniform(1L)\nendaligned","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"where L = textttn_mcmc_steps. Then, we simulate the Markov chain forward and backward as","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"beginalignat*3\n theta_M-l sim Kleft(theta_L-l+1 cdot right) qquad textfor l = 1 ldots M-1 \n theta_l sim Kleft(theta_l-1 cdot right) qquad textfor l = M+1 ldots L\nendalignat*","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"forming the chain","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"theta_1 ldots theta_M ldots theta_L","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"The rank is the ranking of the statistics of theta_M. If the sampler and the model are correct, the rank has an uniform distribution as long as the midpoint is independently sampled.","category":"page"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"ExactRankTest","category":"page"},{"location":"exactranktest/#MCMCTesting.ExactRankTest","page":"Exact Rank Tests","title":"MCMCTesting.ExactRankTest","text":"ExactRankTest(n_samples, n_mcmc_steps; n_mcmc_thin)\n\nExact rank hypothesis testing strategy for reversible MCMC kernels. Algorithm 2 in Gandy & Scott (2021).\n\nArguments\n\nn_samples::Int: Number of ranks to be simulated.\nn_mcmc_steps::Int: Number of MCMC states to be simulated for simulating a single rank.\nn_mcmc_thin::Int: Number of thinning applied to the MCMC chain.\n\nReturns\n\npvalues: P-value computed for each dimension of the statistic returned from statistics.\n\nRequirements\n\nThis test requires the following functions for model and kernel to be implemented:\n\nmarkovchain_transition\nsample_joint\n\nFurthermore, this test explicitly assumes the following\n\nkernel is reversible.\n\nApplying this tests to an irreversible kernel will result in false negatives even if its stationary distribution is correct.\n\nKeyword Arguments for Tests\n\nWhen calling mcmctest or seqmcmctest, this tests has an additional keyword argument:\n\nuniformity_test_pvalue: The p-value calculation strategy.\n\nThe default strategy is an chi^2 test. Any function returning a single p-value from a uniformity hypothesis test will work. The format is as follows:\n\nuniformity_test_pvalue(x::AbstractVector)::Real\n\n\n\n\n\n","category":"type"},{"location":"exactranktest/#References","page":"Exact Rank Tests","title":"References","text":"","category":"section"},{"location":"exactranktest/","page":"Exact Rank Tests","title":"Exact Rank Tests","text":"[GS2021]: Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.","category":"page"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = MCMCTesting","category":"page"},{"location":"#MCMCTesting","page":"Home","title":"MCMCTesting","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Documentation for MCMCTesting.","category":"page"},{"location":"","page":"Home","title":"Home","text":"MCMCTesting provides the MCMC testing algorithms developed by Gandy & Scott (2021)[GS2021]. These tests can be seen as an improvement of the hypothesis testing approach proposed by Geweke [G2004]. Unlike simulation-based calibration (SBC; [TBSVG2018][YD2023][MMKBPBHFGV2022]), these tests are more appropriate for testing the exactness of the MCMC algorithm rather than the identifiability of the models. This is because the tests focus on maximizing the power for verify the validity of individual Markov transitions instead of a set of samples. Furthermore, unlike SBC, the approach of Gandy & Scott[GS2021] is able to exactly satisfy the assumptions required for the theoretical guarantees.","category":"page"},{"location":"#References","page":"Home","title":"References","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"[GS2021]: Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.","category":"page"},{"location":"","page":"Home","title":"Home","text":"[G2004]: Geweke, J. (2004). Getting it right: Joint distribution tests of posterior simulators. Journal of the American Statistical Association, 99(467), 799-804.","category":"page"},{"location":"","page":"Home","title":"Home","text":"[TBSVG2018]: Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2018). Validating Bayesian inference algorithms with simulation-based calibration. arXiv preprint arXiv:1804.06788.","category":"page"},{"location":"","page":"Home","title":"Home","text":"[YD2023]: Yao, Y., & Domke, J. (2023, November). Discriminative Calibration: Check Bayesian Computation from Simulations and Flexible Classifier. In Thirty-seventh Conference on Neural Information Processing Systems.","category":"page"},{"location":"","page":"Home","title":"Home","text":"[MMKBPBHFGV2022]: Modrák, M., Moon, A. H., Kim, S., Bürkner, P., Huurre, N., Faltejsková, K., ... & Vehtari, A. (2022). Simulation-based calibration checking for Bayesian computation: The choice of test quantities shapes sensitivity. arXiv preprint arXiv:2211.02383.","category":"page"},{"location":"example/#tutorial","page":"Tutorial","title":"Tutorial","text":"","category":"section"},{"location":"example/#Problem-Setup","page":"Tutorial","title":"Problem Setup","text":"","category":"section"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"Let's consider a simple Normal-Normal model:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"beginaligned\ntheta_1 sim mathrmnormalleft(0 sigma^2right) \ntheta_2 sim mathrmnormalleft(0 sigma^2right) \ny sim mathrmnormalleft(theta_1 + theta_2 sigma_epsilon^2right)\nendaligned","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"The joint log-likelihood can be implemented as follows:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"using Random\nusing Distributions\n\nstruct Model\n sigma ::Float64\n sigma_eps::Float64\n y ::Float64\nend\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"For sampling from the posterior, a simple Gibbs sampling strategy is possible:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"struct Gibbs end\n\nfunction complete_conditional(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)\n μ = σ²/(σ²_ϵ + σ²)*(y - θ)\n σ = 1/sqrt(1/σ²_ϵ + 1/σ²)\n Normal(μ, σ)\nend\n\nfunction step(rng::Random.AbstractRNG, model::Model, ::Gibbs, θ)\n θ = copy(θ)\n y = model.y\n σ² = model.sigma^2\n σ²_ϵ = model.sigma_eps^2\n θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))\n θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))\n θ\nend\nnothing","category":"page"},{"location":"example/#Testing-the-Gibbs-Sampler","page":"Tutorial","title":"Testing the Gibbs Sampler","text":"","category":"section"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"All of the functionalities of MCMCTesting assume that we can sample from the joint distribution p(theta y). This is done by as follows:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"using MCMCTesting\n\nfunction MCMCTesting.sample_joint(rng::Random.AbstractRNG, model::Model)\n θ₁ = rand(rng, Normal(0, model.sigma))\n θ₂ = rand(rng, Normal(0, model.sigma))\n θ = [θ₁, θ₂]\n y = rand(rng, Normal(θ[1] + θ[2], model.sigma_eps))\n θ, y\nend\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"The Gibbs samplers can be connected to MCMCTesting by implementing the following:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"using Accessors\n\nfunction MCMCTesting.markovchain_transition(\n rng::Random.AbstractRNG, model::Model, kernel, θ, y\n)\n model′ = @set model.y = only(y)\n step(rng, model′, kernel, θ)\nend\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"Let's check that the implementation is correct by ","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"model = Model(1., .5, randn())\nkernel = Gibbs()\ntest = TwoSampleTest(100, 100)\nsubject = TestSubject(model, kernel)\nseqmcmctest(test, subject, 0.0001, 100; show_progress=false)","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"true means that the tests have passed.","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"Now, let's consider two erroneous implementations:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"struct GibbsWrongMean end\n\nfunction complete_conditional_wrongmean(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)\n μ = σ²/(σ²_ϵ + σ²)*(y + θ)\n σ = 1/sqrt(1/σ²_ϵ + 1/σ²)\n Normal(μ, σ)\nend\n\nfunction step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongMean, θ)\n θ = copy(θ)\n y = model.y\n σ² = model.sigma^2\n σ²_ϵ = model.sigma_eps^2\n\n θ[1] = rand(rng, complete_conditional_wrongmean(θ[2], σ², σ²_ϵ, y))\n θ[2] = rand(rng, complete_conditional_wrongmean(θ[1], σ², σ²_ϵ, y))\n θ\nend\n\nstruct GibbsWrongVar end\n\nfunction complete_conditional_wrongvar(θ::Real, σ²::Real, σ²_ϵ::Real, y::Real)\n μ = σ²/(σ²_ϵ + σ²)*(y - θ)\n Normal(μ, sqrt(σ²))\nend\n\nfunction step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongVar, θ)\n θ = copy(θ)\n y = model.y\n σ² = model.sigma^2\n σ²_ϵ = model.sigma_eps^2\n\n if rand(Bernoulli(0.5))\n θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))\n θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))\n else\n θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))\n θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))\n end\n θ\nend\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"The kernel with a wrong mean fails:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"kernel = GibbsWrongMean()\nsubject = TestSubject(model, kernel)\nseqmcmctest(test, subject, 0.0001, 100; show_progress=false)","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"and so does the one with the wrong variance:","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"kernel = GibbsWrongVar()\nsubject = TestSubject(model, kernel)\nseqmcmctest(test, subject, 0.0001, 100; show_progress=false)","category":"page"},{"location":"example/#Visualizing-Simulated-Ranks","page":"Tutorial","title":"Visualizing Simulated Ranks","text":"","category":"section"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"MCMCTesting also provides some basic plot recipes for visualizing the simulated rank for the exact rank test. For this, Plots must be imported before MCMCTesting.","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"using Plots\ngr()\nusing MCMCTesting\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"Also, since the exact rank test explicitly requires the MCMC kernel to be reversible, we modify the previous Gibbs sampler to use a random scan order.","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"function step(rng::Random.AbstractRNG, model::Model, ::Gibbs, θ)\n θ = copy(θ)\n y = model.y\n σ² = model.sigma^2\n σ²_ϵ = model.sigma_eps^2\n if rand(Bernoulli(0.5))\n θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))\n θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))\n else\n θ[2] = rand(rng, complete_conditional(θ[1], σ², σ²_ϵ, y))\n θ[1] = rand(rng, complete_conditional(θ[2], σ², σ²_ϵ, y))\n end\n θ\nend\n\nfunction step(rng::Random.AbstractRNG, model::Model, ::GibbsWrongVar, θ)\n θ = copy(θ)\n y = model.y\n σ² = model.sigma^2\n σ²_ϵ = model.sigma_eps^2\n if rand(Bernoulli(0.5))\n θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))\n θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))\n else\n θ[2] = rand(rng, complete_conditional_wrongvar(θ[1], σ², σ²_ϵ, y))\n θ[1] = rand(rng, complete_conditional_wrongvar(θ[2], σ², σ²_ϵ, y))\n end\n θ\nend\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"Then, we can simulate the ranks and then plot them using Plots.","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"test = ExactRankTest(1000, 10, 10)\n\nrank_correct = simulate_ranks(test, TestSubject(model, Gibbs()); show_progress=false)\nrank_wrong = simulate_ranks(test, TestSubject(model, GibbsWrongVar()); show_progress=false)\n\nstat_names = [\"θ1 mean correct\", \"θ2 mean correct\", \"θ1 var correct\", \"θ2 var correct\"]\nrankplot(test, rank_correct; stat_names)\n\nstat_names = [\"θ1 mean wrong\", \"θ2 mean wrong\", \"θ1 var wrong\", \"θ2 var wrong\"]\nrankplot!(test, rank_wrong; stat_names)\n\nsavefig(\"rankplot.svg\")\nnothing","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"(Image: )","category":"page"},{"location":"example/","page":"Tutorial","title":"Tutorial","text":"If the MCMC kernel under test is reversible and correct, the ranks must resemble samples from a uniform distribution. The colored bands around black line show the 1σ, 2σ, and 3σ deviations from the null hypothesis. Here, we can see that the ranks of the erroneous kernel are not uniform.","category":"page"}] +} diff --git a/v0.3.2/siteinfo.js b/v0.3.2/siteinfo.js new file mode 100644 index 0000000..b2defe1 --- /dev/null +++ b/v0.3.2/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.3.2"; diff --git a/v0.3.2/twosampletest/index.html b/v0.3.2/twosampletest/index.html new file mode 100644 index 0000000..170d2b9 --- /dev/null +++ b/v0.3.2/twosampletest/index.html @@ -0,0 +1,13 @@ + +Two-Sample Tests · MCMCTesting.jl

Two Sample Hypothesis Tests

Introduction

The two-sample hypothesis testing strategies are based on Algorithm 1 by Gandy & Scott (2021)[gandyandscott2021].

TwoSampleTest

The first basic strategy generates the treatment group

\[\begin{aligned} + \theta,\; y_{\text{trtm}} &\sim p\left(\theta, y\right) \\ + \theta_{\text{trtm}} &\sim K\left(\theta, \cdot\right), +\end{aligned}\]

and the control group as

\[\begin{aligned} + \theta_{\text{ctrl}},\; y_{\text{ctrl}} &\sim p\left(\theta, y\right), \\ +\end{aligned}\]

where the test compares

\[(\theta_{\text{trtm}}, \, y_{\text{trtm}}) +\quad\text{versus}\quad +(\theta_{\text{ctrl}}, \, y_{\text{ctrl}}).\]

MCMCTesting.TwoSampleTest — Type
TwoSampleTest(n_samples, n_mcmc_steps; n_control, n_treatment, n_mcmc_thin)

Two-sample hypothesis testing strategy. Algorithm 1 in Gandy & Scott (2021).

Arguments

  • n_samples::Int: Number of samples from the joint p(θ, y) used for the computing the p-values.
  • n_mcmc_steps::Int: Number of times the MCMC kernel is applied to initial sample from the joint. (Increasing this value improves the power of the test.)

Keyword Arguments

  • n_control::Int: Number of pure samples from the joint (control group). (Default: n_samples)
  • n_treatment::Int: Number of samples from the MCMC kernel (treatment group). (Default: n_samples)
  • n_mcmc_thin::Int: Number of thinning applied to the MCMC chain. The effect of this argument is the same as n_mcmc_steps.

Returns

  • pvalues: P-value computed for each dimension of the statistic returned from statistics.

Requirements

This test requires the following functions for model and kernel to be implemented:

  • markovchain_transition
  • sample_joint

Keyword Arguments for Tests

When calling mcmctest or seqmcmctest, this tests has an additional keyword argument:

  • two_sample_test_pvalue: The p-value calculation strategy.

The default strategy is an approximate two-sample Kolmogorov-Smirnov test. Any function returning a single p-value from a two-sample hypothesis test will work. The format is as follows:

two_sample_test_pvalue(x::AbstractVector, y::AbstractVector)::Real
source

TwoSampleGibbsTest

The second strategy performs applies an additional Gibbs sampling step when generating the treatment group as

\[\begin{aligned} + \theta,\; y &\sim p\left(\theta, y\right) \\ + \theta_{\text{trtm}} &\sim K\left(\theta, \cdot\right), \\ + y_{\text{trtm}} &\sim p\left(y \mid \theta_{\text{trtm}}\right) +\end{aligned}\]

resulting in the treatment group

\[(\theta_{\text{trtm}}, \, y_{\text{trtm}}).\]

The control group is generated the same as TwoSampleTest.

To use this test, the user needs to implement the following interface for simulating from the conditional likelihood.

MCMCTesting.sample_predictive — Function
sample_predictive(rng, model, θ)

Sample from the predictive distribution of model conditionally on θ

Arguments

  • rng::Random.AbstractRNG: Random number generator.
  • model: Model subject to test.
  • θ: Model parameters to condition on.

Returns

  • y: Data generated from conditionally on θ from p(y|θ)
source
MCMCTesting.TwoSampleGibbsTest — Type
TwoSampleTest(n_samples, n_mcmc_steps; n_control, n_treatment, n_mcmc_thin)

Two-sample hypothesis testing strategy with an additional Gibbs sampling step. Modified version of Algorithm 1 in Gandy & Scott 2021 for increased power.

Arguments

  • n_samples::Int: Number of samples from the joint p(θ, y) used for the computing the p-values.
  • n_mcmc_steps::Int: Number of times the MCMC kernel is applied to initial sample from the joint. (Increasing this value improves the power of the test.)

Keyword Arguments

  • n_control::Int: Number of pure samples from the joint (control group). (Default: n_samples)
  • n_treatment::Int: Number of samples from the MCMC kernel (treatment group). (Default: n_samples)
  • n_mcmc_thin::Int: Number of thinning applied to the MCMC chain. The effect of this argument is the same as n_mcmc_steps.

Returns

  • pvalues: P-value computed for each dimension of the statistic returned from statistics.

Requirements

This test requires the following functions for model and kernel to be implemented:

  • markovchain_transition
  • sample_joint
  • sample_predictive

Keyword Arguments for Tests

When calling mcmctest or seqmcmctest, this tests has an additional keyword argument:

  • two_sample_test_pvalue: The p-value calculation strategy.

The default strategy is an approximate two-sample Kolmogorov-Smirnov test. Any function returning a p-value to two sample groups will work. The format is as follows:

two_sample_test_pvalue(x::AbstractVector, y::AbstractVector)::Real

References

source

References

  • gandyandscott2021Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465.
diff --git a/versions.js b/versions.js index c04be8f..15aaaec 100644 --- a/versions.js +++ b/versions.js @@ -1,7 +1,8 @@ var DOC_VERSIONS = [ "stable", + "v0.3", "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v0.1.6"; +var DOCUMENTER_NEWEST = "v0.3.2"; var DOCUMENTER_STABLE = "stable";