Implementing Bayesian Inference using MCMC on MINITAB

Abstract

Bayesian paradigm offers a conceptually simple and coherent system of statistical inference based on the simple data structure in representing uncertain knowledge by probability distribution for quantities of interest. The quantities of observed and unobserved data are then be manipulated by using laws of probability, in particular Bayes theorem, to obtain the posterior distribution of the quantity of interest. By using the pragmatic advantages of the Bayesian framework that allow to cope a very complex problems in analytic and dimension become simple in one dimension, this paper emphasize a stochastic simulation and the combination of mathematical analysis and simulation, in particular MCMC approach, as a general methods for summarizing distributions computationally.

The methods of MCMC approaches with their stichastic simulation for Bayesian inference have been developed in macros of the MINITAB-based approaches. Some examples are presented to demonstrate the use of MINITAB for this Bayesian statistical inference. It is shown that for a single parameter the Package is useful for statistical computation, analysis and graphical presentation of the posterior densities. These capabilities show that the package is a suitable, a simple and an appropriate tool for implementing and teaching a computational Bayesian statistical inference using MCMC approach.

Keywords: Markov Chain Monte Carlo, Bayesian methods, Rejection Sampling, Full conditional density, Marginal posterior density, MINITAB macros.