bayes_dice/bayes_dice.html

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      BAYES_DICE: Bayesian Dice Estimation
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      BAYES_DICE <br> Bayesian Dice Estimation
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    <p>
      <b>BAYES_DICE</b>
      is a FORTRAN90 program which
      performs a simple demonstration of Bayesian Statistics.
    </p>

    <p>
      Suppose we're watching a "system" and trying to analyze its
      behavior.  Each time we observe the system, it rolls a die a
      certain number of times, and reports the results.  We want to
      estimate THETA(1) through THETA(6), the probabilities of each result.
    </p>

    <p>
      We treat the values of THETA as random variables themselves,
      controlled by a Dirichlet probability density function with
      parameters ALPHA(1) through ALPHA(6).  We make an arbitrary
      guess for initial ALPHA values.  We observe the system and
      adjust the ALPHA's using Bayes's Law.
    </p>

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      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>

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      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_weight/bayes_weight.html">
      BAYES_WEIGHT</a>,
      a FORTRAN90 program which
      uses Bayesian analysis to estimate the probabilities that one or
      another of two weighted dice is chosen.
    </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_dice.f90">bayes_dice.f90</a>, the source code;
        </li>
        <li>
          <a href = "bayes_dice.sh">bayes_dice.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_dice_output.txt">bayes_dice_output.txt</a>, a sample run;
        </li>
      </ul>
    </p>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>BAYES_DICE</b> does a simple demonstration of Bayesian statistics.
        </li>
        <li>
          <b>TEST01</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_SAMPLE</b> samples the Discrete PDF.
        </li>
        <li>
          <b>R8_RANDOM</b> returns a random R8 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 30 December 2007.
    </i>

    <!-- John Burkardt -->

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