# Bayesian regression analysis.

5-2012

Master's Thesis

M.A.

Mathematics

## Committee Chair

Sahoo, Prasanna K.

## Author's Keywords

Frequentist regression; Bayes' theorem; Bayesian regression

## Subject

Bayesian statistical decision theory; Regression analysis

## Abstract

Regression analysis is a statistical method used to relate a variable of interest, typically y (the dependent variable), to a set of independent variables, usually, X1, X2,...,Xn . The goal is to build a model that assists statisticians in describing, controlling, and predicting the dependent variable based on the independent variable(s). There are many types of regression analysis: Simple and Multiple Linear Regression, Nonlinear Regression, and Bayesian Regression Analysis to name a few. Here we will explore simple and multiple linear regression and Bayesian linear regression. For years, the most widely used method of regression analysis has been the Frequentist methods, or simple and multiple regression. However, with the advancements of computers and computing tools such as WinBUGS, Bayesian methods have become more widely accepted. With the use of WinBUGS, we can utilize a Markov Chain Monte Carlo (MCMC) method called Gibbs Sampling to simplify the increasingly difficult calculations. Given that Bayesian regression analysis is a relatively "new" method, it is not without faults. Many in the statistical community find that the use of Bayesian techniques is not a satisfactory method since the choice of the prior distribution is purely a guessing game and varies from statistician to statistician. In this thesis, an example is presented using both Frequentist and Bayesian methods and a comparison is made between the two. As computers become more advanced, the use of Bayesian regression analysis may become more widely accepted as the method of choice for regression analyses as it allows for the interpretation of a "probability as a measure of degree of belief concerning actual data observed."

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