bayes_weight/bayes_weight.html

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    <title>
      BAYES_WEIGHT - Estimate Mixture PDF Weights
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      BAYES_WEIGHT <br> Estimate Mixture PDF Weights
    </h1>

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    <p>
      <b>BAYES_WEIGHT</b>
      is a FORTRAN90 program which
      demonstrates Bayesian analysis.
    </p>

    <p>
      The program estimates the weights used in a mixture probability density
      function (PDF).  In the case examined here, the parameters of
      the PDF's are known, but the mixing weights are not.  It is
      the task of the program to observe the system and estimate these
      weights.
    </p>

    <p>
      Each event will be a roll of a die.  We have two dice to choose from,
      each with a different characteristic probability density function.
      For each event, the probability we will choose die #1 or die #2 are
      the unknowns W1 and W2.  We start with a guess for these values,
      but after each roll, we adjust our guesses based on the product of
      the likelihoods of observing this result given that density,
      and our previously estimated likelihood of that density.
    </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_beta/bayes_beta.html">
      BAYES_BETA</a>,
      a FORTRAN90 program which
      uses Bayesian analysis to estimate the parameters in a beta distribution
      based on a series of sample data.
    </p>

    <p>
      <a href = "../../f_src/bayes_dice/bayes_dice.html">
      BAYES_DICE</a>,
      a FORTRAN90 program which
      uses Bayesian analysis to estimate the probabilities of a weighted die.
    </p>

    <p>
      <a href = "../../f_src/dcdflib/dcdflib.html">
      DCDFLIB</a>,
      a FORTRAN90 library which
      evaluates and inverts
      a number of statistical distributions.
    </p>

    <p>
      <a href = "../../cpp_src/gsl/gsl.html">
      GSL</a>,
      a C++ library which
      includes many routines for evaluating
      probability distributions.
    </p>

    <p>
      <a href = "../../f_src/normal/normal.html">
      NORMAL</a>,
      a FORTRAN90 library which
      samples the normal distribution.
    </p>

    <p>
      <a href = "../../f_src/prob/prob.html">
      PROB</a>,
      a FORTRAN90 library which
      evaluates the PDF, CDF, mean and variance for a number of probability
      density functions.
    </p>

    <p>
      <a href = "../../f_src/uniform/uniform.html">
      UNIFORM</a>,
      a FORTRAN90 library which
      samples the uniform distribution.
    </p>

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      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "bayes_weight.f90">bayes_weight.f90</a>, the source code;
        </li>
        <li>
          <a href = "bayes_weight.sh">bayes_weight.sh</a>,
          commands to compile and load the source code;
        </li>
      </ul>
    </p>

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "bayes_weight_output.txt">bayes_weight_output.txt</a>,
          the output file;
        </li>
      </ul>
    </p>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>BAYES_WEIGHT</b> does a simple demonstration of Bayesian statistics.
        </li>
        <li>
          <b>DIRICHLET_MEAN</b> returns the means of the Dirichlet PDF.
        </li>
        <li>
          <b>DISCRETE_CDF_INV</b> inverts the Discrete CDF.
        </li>
        <li>
          <b>DISCRETE_PDF</b> evaluates the Discrete PDF.
        </li>
        <li>
          <b>DISCRETE_SAMPLE</b> samples the Discrete PDF.
        </li>
        <li>
          <b>RVEC_PRINT</b> prints a real vector, with an optional title.
        </li>
        <li>
          <b>R_RANDOM</b> returns a random real in a given range.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

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    <i>
      Last revised on 23 August 2008.
    </i>

    <!-- John Burkardt -->

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