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bayes_beta.html
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<html>
<head>
<title>
BAYES_BETA: Bayesian Parameter Estimation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BAYES_BETA <br> Bayesian Parameter Estimation
</h1>
<hr>
<p>
<b>BAYES_BETA</b>
if a FORTRAN90 program which
is a simple Bayesian Statistics demonstration.
</p>
<p>
Suppose we're watching a "system" and trying to analyze its behavior.
Each time we observe the system, it flips a coin a certain number of
times, and reports the number of heads and tails. We want to estimate
THETA1 and THETA2, the probabilities of heads and of tails.
</p>
<p>
We treat the values of THETA1 and THETA2 as random variables
themselves, controlled by a Beta probability density function, which has
parameters ALPHA1 and ALPHA2. We make an arbitrary or informed guess
for initial values of ALPHA1 and ALPHA2. We observe the system,
and adjust ALPHA1 and ALPHA2 using Bayes's Law. We continue until
we are satisfied that our estimates seem to have converged.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/bayes_dice/bayes_dice.html">
BAYES_DICE</a>,
a FORTRAN90 program which
uses Bayesian analysis to adjust a model of loaded dice
based on a sequence of experimental observations.
</p>
<p>
<a href = "../../f_src/bayes_weight/bayes_weight.html">
BAYES_WEIGHT</a>,
a FORTRAN90 program which
uses Bayesian analysis to adjust a model of loaded dice
based on a sequence of experimental observations.
</p>
<p>
<a href = "../../f_src/bdmlib/bdmlib.html">
BDMLIB</a>,
a FORTRAN90 library which
estimates the weights in a Dirichlet mixtured based on sample data;
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bayes_beta.f90">bayes_beta.f90</a>, the source code;
</li>
<li>
<a href = "bayes_beta.sh">bayes_beta.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "bayes_beta_output.txt">bayes_beta_output.txt</a>, a sample run;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BAYES_BETA</b> does a simple demonstration of Bayesian statistics.
</li>
<li>
<b>TEST01</b> does a simple demonstration of Bayesian statistics.
</li>
<li>
<b>BETA</b> returns the value of the Beta function.
</li>
<li>
<b>BETA_MAX</b> returns the most likely values of T1 and T2 for a Beta PDF.
</li>
<li>
<b>BETA_PDF</b> returns the value of the Beta probability density function.
</li>
<li>
<b>BETA_PLOT</b> "plots" the Beta distribution for given parameters.
</li>
<li>
<b>LOG_GAMMA</b> calculates the natural logarithm of GAMMA ( X ) for positive X.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 30 August 2005.
</i>
<!-- John Burkardt -->
</body>
</html>