A Bayesian framework for analysis of probability distributions

Abstract

Statistics, as a discipline, is mostly concerned with making inferences about the events actually occurring in the real world. It consists of two main competing schools of thought: the frequentists or classical approach to statistical inference, and the Bayesian approach. Bayesian paradigm is concerned with generating the posterior distribution of the unknown parameters given both the data and some prior density for these parameters. The parameters are considered to be random variables and the posterior distribution provides a much more complete picture of the uncertainty in the estimation of the unknown parameters. Bayesian inference has shown strong growth in the recent years due to introduction of new numerical algorithms for estimation purposes and faster developments in computing technology. The special situation arising in scientific reporting and public decision making where the only acceptable information, is that which may be deduced from available documented data, is usually addressed by Bayesian methods. newline