Bayes factor: hypothesis testing in restricted Stein-rule regression analysis with autocorrelated

Abstract

Regression is a generic tool used to make inferences so as to draw logical conclusions and judgments about a particular problem. It has been widely used in engineering, sciences, education, technology, and social sciences for a long time. Breaking down of the underlying estimation mar the judgment and decision of the study. Chiefly among the error structure that can lead to the drawback of the inferences of regression is the autocorrelation of error term of both AR and MA processes. Restricted Stein-rule regression analysis was used with data injected with autocorrelated error; H1 was modeled with autocorrelated error whereas H0 was modeled without, alternative approach in Bayes factor of AR(1) and MA(1) processes were introduced and compared with Bayesian information criterion approach in both negative and positive r (symmetrical). The choice of the Bayes factor (Bf) is due to the probabilistic nature of Bayesian inference, which over the years has been performed better than the classical approach. The datasets with five covariates was set at 25 to capture the error structure and project the property of a small sample. The study, therefore, concluded that Bayesian inference being probabilistic about the uncertainty of the parameters should be adopted to verify the presence or absence of autocorrelated error in the data before estimation.