BAYES_BETA: Bayesian Parameter Estimation

BAYES_BETA is a simple Bayesian Statistics demonstration.

Suppose we're watching a "system" and trying to analyze its behavior. Each time we observe the system, it flips a coin a certain number of times, and reports the number of heads and tails. We want to estimate THETA1 and THETA2, the probabilities of heads and of tails.

We treat the values of THETA1 and THETA2 as random variables themselves, controlled by a Beta probability density function, which has parameters ALPHA1 and ALPHA2. We make an arbitrary or informed guess for initial values of ALPHA1 and ALPHA2. We observe the system, and adjust ALPHA1 and ALPHA2 using Bayes's Law. We continue until we are satisfied that our estimates seem to have converged.

Files you may copy include:

• bayes_beta.f90, the source code;
• bayes_beta.out, a sample run;

The list of routines includes:

• BAYES_BETA does a simple demonstration of Bayesian statistics.
• TEST01 does a simple demonstration of Bayesian statistics.
• BETA returns the value of the Beta function.
• BETA_MAX returns the most likely values of T1 and T2 for a Beta PDF.
• BETA_PDF returns the value of the Beta probability density function.
• BETA_PLOT "plots" the Beta distribution for given parameters.
• LOG_GAMMA calculates the natural logarithm of GAMMA ( X ) for positive X.

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