BAYES_WEIGHT
Estimate Mixture PDF Weights

BAYES_WEIGHT is a FORTRAN90 program which demonstrates Bayesian analysis.

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.

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BAYES_WEIGHT is available in a FORTRAN90 version.

Related Data and Programs:

BAYES_BETA, a FORTRAN90 program which uses Bayesian analysis to estimate the parameters in a beta distribution based on a series of sample data.

BAYES_DICE, a FORTRAN90 program which uses Bayesian analysis to estimate the probabilities of a weighted die.

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

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

NORMAL, a FORTRAN90 library which samples the normal distribution.

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

UNIFORM, a FORTRAN90 library which samples the uniform distribution.

Source Code:

• bayes_weight.f90, the source code;
• bayes_weight.sh, commands to compile and load the source code;

Examples and Tests:

• bayes_weight_output.txt, the output file;

List of Routines:

• 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.
• R_RANDOM returns a random real 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.