diff --git a/Logbook.md b/Logbook.md index 232a164d..69c3118f 100644 --- a/Logbook.md +++ b/Logbook.md @@ -1,5 +1,17 @@ ## 2024-02-14 +### BB on testing statistical properties + +1. Ran and statistically analyzed an experiment [using this Jupyter notebook](peras-iosim/analyses/block-production/ReadMe.ipynb) to verify the correctness of slot leadership and block production for the `PseudoPraos` protocol. +2. Research QuickCheck-based approaches for handling approximate equality and statistical properties. + - There don't seem to be special-purpose libraries of this. + - QuickCheck and its extension provide some control over coverage and sampling, but this doesn't address the fundamental problem of determining when a failure is a valid statistical outlier vs an error. +3. Revised QuickCheck test for block production to use a three-sigma confidence interval. Eventually, we'll need to make the sigma level tunable. + +Other revisions to `peras-iosim`: +- Added an explicit parameter for total stake to `Peras.IOSim.Simulate.Types.Parameters`. +- Changed serialization of `Peras.Chain` so that it doesn't keeply next JSON, since that causes most JSON parsers to crash for long chains. + ### AB on Network Modeling Reading about Rust's FFI: https://www.michaelfbryan.com/rust-ffi-guide/setting_up.html diff --git a/peras-iosim/analyses/block-production/ReadMe.ipynb b/peras-iosim/analyses/block-production/ReadMe.ipynb new file mode 100644 index 00000000..7251d9be --- /dev/null +++ b/peras-iosim/analyses/block-production/ReadMe.ipynb @@ -0,0 +1,660 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b5a996b5-2079-42a8-a904-5ddac6952532", + "metadata": {}, + "source": [ + "# Statistical analysis of slot leadership in `peras-iosim`\n", + "\n", + "This notebook is best viewed at https://nbviewer.org/." + ] + }, + { + "cell_type": "markdown", + "id": "1fc2bee6-8d6a-4e44-ac8b-c46aca134306", + "metadata": {}, + "source": [ + "## Load required packages" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "7683c5c5-8a56-4f4b-88ac-67bd7a373ac2", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Loading required package: data.table\n", + "\n", + "Loading required package: ggplot2\n", + "\n", + "Loading required package: magrittr\n", + "\n" + ] + } + ], + "source": [ + "require(data.table)\n", + "require(ggplot2)\n", + "require(magrittr)" + ] + }, + { + "cell_type": "markdown", + "id": "bbab57c4-fb18-4ac3-bc1d-06aa81d89036", + "metadata": {}, + "source": [ + "## Read experimental results\n", + "\n", + "The experiment was created from using the [experiment.sh](experiment.sh) script." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "52e36f53-eee1-4a9b-8ad2-b5c9c5b31f8a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + " Seed Active Slot Coefficient End Slot Total Stake \n", + " Min. : 11 Min. :0.05 Min. :7200 Min. :1000 \n", + " 1st Qu.: 8729 1st Qu.:0.05 1st Qu.:7200 1st Qu.:1000 \n", + " Median :16728 Median :0.05 Median :7200 Median :1000 \n", + " Mean :16780 Mean :0.05 Mean :7200 Mean :1000 \n", + " 3rd Qu.:24906 3rd Qu.:0.05 3rd Qu.:7200 3rd Qu.:1000 \n", + " Max. :32737 Max. :0.05 Max. :7200 Max. :1000 \n", + " Node Stake Blocks Produced\n", + " Min. : 1.0 Min. : 0.0 \n", + " 1st Qu.: 256.0 1st Qu.: 92.0 \n", + " Median : 494.5 Median :182.0 \n", + " Mean : 503.6 Mean :182.0 \n", + " 3rd Qu.: 761.5 3rd Qu.:276.2 \n", + " Max. :1000.0 Max. :394.0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results <- fread(\"results.csv\")\n", + "results %>% summary" + ] + }, + { + "cell_type": "markdown", + "id": "25bfd225-558b-4a07-8a51-b9260278d715", + "metadata": {}, + "source": [ + "### Extract the simulation parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f21d33b1-8e9e-4c49-b418-6aadaf766b79", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "0.05" + ], + "text/latex": [ + "0.05" + ], + "text/markdown": [ + "0.05" + ], + "text/plain": [ + "[1] 0.05" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "activeSlotCoefficient <- results[1, `Active Slot Coefficient`]\n", + "activeSlotCoefficient" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6c2bcda5-b402-42c1-babd-59d9999f9b54", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "1000" + ], + "text/latex": [ + "1000" + ], + "text/markdown": [ + "1000" + ], + "text/plain": [ + "[1] 1000" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "totalStake <- results[1, `Total Stake`]\n", + "totalStake" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6c86330d-071f-4152-8011-4e92d259607a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "7200" + ], + "text/latex": [ + "7200" + ], + "text/markdown": [ + "7200" + ], + "text/plain": [ + "[1] 7200" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "slotCount <- results[1, `End Slot`]\n", + "slotCount" + ] + }, + { + "cell_type": "markdown", + "id": "b794f97c-72e3-4caf-811e-b1e8c1d14058", + "metadata": {}, + "source": [ + "## Compute the distribution of expected number of blocks produced" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ec59bca6-f65c-42b7-a533-3e7bd4cb7997", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "pBlock <- function(stake) {\n", + " 1 - (1 - activeSlotCoefficient)^(stake / totalStake)\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a722be30-fc73-4e25-851c-763e588ddd4f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.table: 6 x 3
Node StakeProbabilityBlocks Produced
<dbl><dbl><dbl>
10.0010
10.0100
10.0500
10.9502
10.9902
10.9993
\n" + ], + "text/latex": [ + "A data.table: 6 x 3\n", + "\\begin{tabular}{lll}\n", + " Node Stake & Probability & Blocks Produced\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\t 1 & 0.001 & 0\\\\\n", + "\t 1 & 0.010 & 0\\\\\n", + "\t 1 & 0.050 & 0\\\\\n", + "\t 1 & 0.950 & 2\\\\\n", + "\t 1 & 0.990 & 2\\\\\n", + "\t 1 & 0.999 & 3\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.table: 6 x 3\n", + "\n", + "| Node Stake <dbl> | Probability <dbl> | Blocks Produced <dbl> |\n", + "|---|---|---|\n", + "| 1 | 0.001 | 0 |\n", + "| 1 | 0.010 | 0 |\n", + "| 1 | 0.050 | 0 |\n", + "| 1 | 0.950 | 2 |\n", + "| 1 | 0.990 | 2 |\n", + "| 1 | 0.999 | 3 |\n", + "\n" + ], + "text/plain": [ + " Node Stake Probability Blocks Produced\n", + "1 1 0.001 0 \n", + "2 1 0.010 0 \n", + "3 1 0.050 0 \n", + "4 1 0.950 2 \n", + "5 1 0.990 2 \n", + "6 1 0.999 3 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "probs <- CJ(\n", + " `Node Stake`=c(1,2,5,10,20,50,100,200,500,1000),\n", + " `Probability`=c(0.001, 0.01, 0.05, 0.95, 0.99, 0.999)\n", + ")\n", + "probs[, `Blocks Produced`:=mapply(function(s, p) qbinom(p, slotCount, pBlock(s)), `Node Stake`, `Probability`)]\n", + "probs %>% head" + ] + }, + { + "cell_type": "markdown", + "id": "125e4fdc-389a-424d-8e3d-59d6f4174d7a", + "metadata": {}, + "source": [ + "## Compare the experimental results to the probability contours" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "72e28c69-4103-40b3-949d-8fc732336b56", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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Xs2KCjo1Vdf/SIj6+vMrBo8t65mqDer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9dv376VENt36HXIfFTHcaIrF8Rnf+OkMu2EqSiq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SiYSO8Hg8hUKh1WrPnz9/fw4sFis/P//WrVv19fUZ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\nAICNQGMHAAAAYCPQ2AEAAADYiH8BuUyAQeturEMAAAAASUVORK5CYII=", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ggplot(probs, aes(x=`Node Stake`, y=`Blocks Produced`)) +\n", + " geom_line(aes(group=factor(`Probability`), color=factor(`Probability`))) +\n", + " labs(color=\"Probability\") +\n", + " geom_point(data=results, aes(x=`Node Stake`, y=`Blocks Produced`), size=0.5)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "276dd30b-1e89-4d70-9688-cd8ac8ddfd57", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "ggsave(\"stake-blocks.png\", width=6, height=4, units=\"in\")" + ] + }, + { + "cell_type": "markdown", + "id": "b3a7e962-bb5f-474c-be08-3f8122540e8f", + "metadata": {}, + "source": [ + "## Plot the empirically observed quantiles" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "4766af47-e294-46a7-b56a-576557defb68", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "results[, `Quantile`:=mapply(function(s, q) pbinom(q, slotCount, pBlock(s)), `Node Stake`, `Blocks Produced`)]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "021eb17b-df9a-442f-84c7-ac13cce4119d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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iKVvpiTGxApIBIilb6YkxsQKSASIpW+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\n4slpa2uRXnMyIm0ViDS73Nr7veGHR190/rS1tUgRRNoaEGl2edU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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ggplot(results, aes(x=`Quantile`)) +\n", + " geom_histogram(bins=100)" + ] + }, + { + "cell_type": "markdown", + "id": "80c6fc41-8953-4d49-b6f6-9aaf69c9df50", + "metadata": {}, + "source": [ + "This looks pretty uniform, but let's quantify that." + ] + }, + { + "cell_type": "markdown", + "id": "937add3d-d651-4349-b301-f3e2a89d57eb", + "metadata": {}, + "source": [ + "## Perform a Kolmogorov-Smirnov test\n", + "\n", + "This test checks whether the data's quantiles are uniformly distributed. If they are, then the block production count is consistent with a binomial distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "0e20104e-1f54-43a2-a16e-5db576c2a358", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Warning message in ks.test.default(results$Quantile, \"punif\", min = 0, max = 1):\n", + "“ties should not be present for the Kolmogorov-Smirnov test”\n" + ] + }, + { + "data": { + "text/plain": [ + "\n", + "\tAsymptotic one-sample Kolmogorov-Smirnov test\n", + "\n", + "data: results$Quantile\n", + "D = 0.023265, p-value = 0.6587\n", + "alternative hypothesis: two-sided\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ks.test(results$`Quantile`, \"punif\", min=0, max=1)" + ] + }, + { + "cell_type": "markdown", + "id": "9edd06c5-35a0-477d-91ac-376dce8e5b46", + "metadata": {}, + "source": [ + "🙂 The *p*-value of 0.66 indicates no difference from a uniform distribution." + ] + }, + { + "cell_type": "markdown", + "id": "53b8f652-98d3-4deb-81eb-bbadaf2dc608", + "metadata": {}, + "source": [ + "## How accurate is the normal approximation to this binomial distribution?\n", + "\n", + "We might not want to use exact results for the binomial distribution because we need the inverse incomplete beta function for that. Can we approximate by a normal distribution?\n", + "\n", + "The variance of a binomial distribution is $n p (1 - p)$." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "14ae38a8-bb5a-44b6-a5f8-3f60a8288cc1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 0.0253205655191037
  2. 182.308071737546
  3. 13.3301135877551
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 0.0253205655191037\n", + "\\item 182.308071737546\n", + "\\item 13.3301135877551\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 0.0253205655191037\n", + "2. 182.308071737546\n", + "3. 13.3301135877551\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 0.02532057 182.30807174 13.33011359" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p <- pBlock(500)\n", + "xmean <- slotCount * p\n", + "xsd <- sqrt(slotCount * p * (1 - p))\n", + "c(p, xmean, xsd)" + ] + }, + { + "cell_type": "markdown", + "id": "dff5b771-a5c0-44d4-bcbc-7513da99529a", + "metadata": {}, + "source": [ + "Compute quantiles of the normal approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a67454dc-0ac8-49ae-9333-aa57b7d5f4c6", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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  5. 213.318553143144
  6. 223.501219391314
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 141.114924083779\n", + "\\item 151.297590331949\n", + "\\item 160.381986055052\n", + "\\item 204.234157420041\n", + "\\item 213.318553143144\n", + "\\item 223.501219391314\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 141.114924083779\n", + "2. 151.297590331949\n", + "3. 160.381986055052\n", + "4. 204.234157420041\n", + "5. 213.318553143144\n", + "6. 223.501219391314\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 141.1149 151.2976 160.3820 204.2342 213.3186 223.5012" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xqs <- qnorm(c(0.001, 0.01, 0.05, 0.95, 0.99, 0.999), xmean, xsd)\n", + "xqs" + ] + }, + { + "cell_type": "markdown", + "id": "96837235-6f31-4508-b2cc-44a9e63321e4", + "metadata": {}, + "source": [ + "Now compute the actual propabilities corresponding to those approximate quantiles." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "bac4306e-0acd-49a2-aa9b-60e6ddc6968a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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  5. 0.989011746315747
  6. 0.998640324475489
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 0.000756604536561336\n", + "\\item 0.00895997267665929\n", + "\\item 0.0487258867953226\n", + "\\item 0.950026200143427\n", + "\\item 0.989011746315747\n", + "\\item 0.998640324475489\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 0.000756604536561336\n", + "2. 0.00895997267665929\n", + "3. 0.0487258867953226\n", + "4. 0.950026200143427\n", + "5. 0.989011746315747\n", + "6. 0.998640324475489\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 0.0007566045 0.0089599727 0.0487258868 0.9500262001 0.9890117463\n", + "[6] 0.9986403245" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pbinom(xqs, slotCount, p)" + ] + }, + { + "cell_type": "markdown", + "id": "c37bffe8-98b3-4b8a-94b3-fa2fe2a920af", + "metadata": {}, + "source": [ + "The 1%, 5%, 95%, and 99% levels are pretty accurate, but the 0.1% and 99.9% ones are less accurate, but still acceptable for many uses." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "r-minimal kernel", + "language": "r", + "name": "r-minimal" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.2.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/peras-iosim/analyses/block-production/experiment.sh b/peras-iosim/analyses/block-production/experiment.sh new file mode 100755 index 00000000..2630e8e6 --- /dev/null +++ b/peras-iosim/analyses/block-production/experiment.sh @@ -0,0 +1,40 @@ +#/usr/bin/env bash + +PERAS_IOSIM=../../../dist-newstyle/build/x86_64-linux/ghc-9.6.3/peras-iosim-0.1.0.0/x/peras-iosim/noopt/build/peras-iosim/peras-iosim + +cat << EOI > tmp-results.csv +Seed,Active Slot Coefficient,End Slot,Total Stake,Node Stake,Blocks Produced +EOI + +for i in {1..1000} +do + +SEED=$RANDOM +TOTAL_STAKE=1000 +END_SLOT=7200 +ASC=0.05 + +cat << EOI > tmp-network.yaml +randomSeed: $SEED +peerCount: 1 +downstreamCount: 0 +totalStake: $TOTAL_STAKE +maximumStake: $TOTAL_STAKE +messageDelay: 0.35 +endSlot: $END_SLOT +EOI + +cat << EOI > tmp-protocol.yaml +protocol: PseudoPraos +activeSlotCoefficient: $ASC +EOI + +echo "$i: $SEED" + +"$PERAS_IOSIM" --parameter-file tmp-network.yaml --protocol-file tmp-protocol.yaml --result-file tmp-result.json + +jq -r '.exitStates.N1 | "'"$SEED","$ASC","$END_SLOT","$TOTAL_STAKE"',\(.stake),\(.preferredChain.blocks|length)"' tmp-result.json >> tmp-results.csv + +done + +sort -ur tmp-results.csv > results.csv diff --git a/peras-iosim/analyses/block-production/results.csv b/peras-iosim/analyses/block-production/results.csv new file mode 100644 index 00000000..ac3152a2 --- /dev/null +++ b/peras-iosim/analyses/block-production/results.csv @@ -0,0 +1,989 @@ +Seed,Active Slot Coefficient,End Slot,Total Stake,Node Stake,Blocks Produced +9979,0.05,7200,1000,927,352 +9888,0.05,7200,1000,375,154 +9787,0.05,7200,1000,300,93 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+10151,0.05,7200,1000,513,204 +1008,0.05,7200,1000,472,193 +10076,0.05,7200,1000,489,158 +1006,0.05,7200,1000,879,331 +10046,0.05,7200,1000,849,289 +10018,0.05,7200,1000,743,254 +10009,0.05,7200,1000,103,40 diff --git a/peras-quickcheck/peras-quickcheck.cabal b/peras-quickcheck/peras-quickcheck.cabal index 127bb024..be6ebdf9 100644 --- a/peras-quickcheck/peras-quickcheck.cabal +++ b/peras-quickcheck/peras-quickcheck.cabal @@ -61,6 +61,7 @@ library -- Modules exported by the library. exposed-modules: Peras.NetworkModel Peras.NodeModel + other-modules: Data.Statistics.Util -- Modules included in this library but not exported. -- other-modules: diff --git a/peras-quickcheck/src/Data/Statistics/Util.hs b/peras-quickcheck/src/Data/Statistics/Util.hs new file mode 100644 index 00000000..2b0bdcd1 --- /dev/null +++ b/peras-quickcheck/src/Data/Statistics/Util.hs @@ -0,0 +1,38 @@ +module Data.Statistics.Util where + +-- | Check whether a value falls within the central portion of a binomial distribution. +equalsBinomialWithinTails :: + -- | The sample size. + Int -> + -- | The binomial propability. + Double -> + -- | The number of sigmas that define the central acceptance portion. + Double -> + -- | The actual observation. + Int -> + -- | Whether the observation falls within the central region. + Bool +equalsBinomialWithinTails trials probability sigmas actual = + equalsNormalWithinTails + (fromIntegral trials * probability) + (fromIntegral trials * probability * (1 - probability)) + sigmas + (fromIntegral actual) + +-- | Check whether a value falls within the central portion of a normal distribution. +equalsNormalWithinTails :: + -- | The mean. + Double -> + -- | The variance. + Double -> + -- | The number of sigmas that define the central acceptance portion. + Double -> + -- | The actual observation. + Double -> + -- | Whether the observation falls within the central region. + Bool +equalsNormalWithinTails mean variance sigmas actual = + let + spread = sigmas * sqrt variance + in + mean - spread <= actual && actual <= mean + spread diff --git a/peras-quickcheck/src/Peras/NodeModel.hs b/peras-quickcheck/src/Peras/NodeModel.hs index 6b7afd90..f0eab830 100644 --- a/peras-quickcheck/src/Peras/NodeModel.hs +++ b/peras-quickcheck/src/Peras/NodeModel.hs @@ -26,6 +26,7 @@ import Control.Monad.Trans (MonadTrans (..)) import Data.Maybe (fromMaybe) import Data.Ratio (Ratio, (%)) import qualified Data.Set as Set +import Data.Statistics.Util (equalsBinomialWithinTails) import GHC.Generics (Generic) import Numeric.Natural (Natural) import Peras.Block (Block, Slot) @@ -184,5 +185,9 @@ produceExpectedNumberOfBlocks stakeRatio blocks slot = <> show slot monitorPost $ tabulate "# Blocks" ["<= " <> show ((blocks `div` 100 + 1) * 100)] pure $ - actualBP > 0.9 * expectedBP - && actualBP <= 1.1 * expectedBP + equalsBinomialWithinTails + (fromIntegral slot) -- The sample size. + (1 - (1 - defaultActiveSlotCoefficient) ** fromRational stakeRatio) -- Praos probability. + 3 -- Three standard deviations corresponds to the confidence interval from 0.3% to 99.7%. + -- That means that the test will fail after a few batches of 100 tests. + actualBP