BAYES_WEIGHT - Estimate Mixture PDF Weights

BAYES_WEIGHT demonstrates the use of Bayesian analysis to estimate 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.

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.

Files you may copy include:

• bayes_weight.f90, the source code;
• bayes_weight.out, output from a run;

The list of routines includes:

• BAYES_WEIGHT does a simple demonstration of Bayesian statistics.
• DIRICHLET_MEAN returns the means of the Dirichlet PDF.
• DISCRETE_CDF_INV inverts the Discrete CDF.
• DISCRETE_PDF evaluates the Discrete PDF.
• DISCRETE_SAMPLE samples the Discrete PDF.
• RVEC_PRINT prints a real vector, with an optional title.

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