Numerical Methods for Bayesian Analysis

Abstract

Bayesian Inference is a technique of statistical inference that, in addition to using the sample information, utilizes prior information about Parameter(s) to draw results about the Parameters. But the beauty is subdued by huge and cumbersome algebraic calculations necessary to find Posterior estimates. This article suggests numerical methods to derive Posterior distributions under all types of priors – uninformative and informative – and to find Bayes Estimates. We use both numerical differentiation and numerical integration to serve the purpose. The entire estimation procedure is illustrated using real as well as simulated datasets.