Adaptive fuzzy priors for Bayesian inference

Abstract

A fuzzy rule-based system can model prior probabilities in Bayesian inference and thereby approximate posterior probabilities. This fuzzy technique allows users to express prior descriptions in words rather than as closed-form probability density functions. Learning algorithms can tune the expert rules as well as grow them from sample data. The learning laws and closed-form approximations have a tractable form because of the convex-sum structure of additive fuzzy systems. Simulations demonstrate the fuzzy approximation of priors and posteriors for the three most common conjugate priors. An approximate beta prior combines with binomial data to give a new approximate beta posterior. An approximate gamma prior combines with Poisson data to give a new approximate gamma posterior. An approximate normal prior combines with normal data to give a new approximate normal posterior.