BAYES_DICE
Bayesian Dice Estimation

BAYES_DICE is a simple Bayesian Statistics demonstration written in FORTRAN90.

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.

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.

Related Data and Programs:

DCDFLIB is a FORTRAN90 library which evaluates and inverts a number of statistical distributions.

DIRICHLET is a FORTRAN90 library which computes properties of the Dirichlet probability distribution.

GSL is a C++ library which includes many routines for evaluating probability distributions.

NORMAL is a FORTRAN90 library which samples the normal distribution.

PROB is a FORTRAN90 library which evaluates the PDF, CDF, mean and variance for a number of probability density functions.

UNIFORM is a FORTRAN90 library which samples the uniform distribution.

Source Code:

• bayes_dice.f90, the source code;
• bayes_dice.csh, commands to compile and load the source code;

Examples and Tests:

• bayes_dice_output.txt, a sample run;

List of Routines:

• BAYES_DICE does a simple demonstration of Bayesian statistics.
• TEST01 does a simple demonstration of Bayesian statistics.
• DIRICHLET_MEAN returns the means of the Dirichlet PDF.
• DISCRETE_CDF_INV inverts the Discrete CDF.
• DISCRETE_SAMPLE samples the Discrete PDF.
• R8_RANDOM returns a random R8 in a given range.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.