SENSITIVITY ANALYSIS OF PRIOR DISTRIBUTION ON BAYESIAN LINEAR REGRESSION MODEL

Abstract

This research work focused on Bayesian Linear Regression using sensitivity analysis of prior distribution. A sensitivity analysis allows to examine the final model results, based on the original prior, in relation to result that would be obtain using different priors. Perhaps, the regression model is the workhorse of econometrics. In Bayesian Statistical inference, a prior probability distribution of an uncertain quantity is the probability distribution that expresses uncertainty about the quantity before the data are taken into account. The parameters of the prior distribution are called hyper- parameters that distinguish them from parameter of the model of the data. In this study, the researcher reviewed the growth of the economy of a country has been determined by the Gross Domestic Product (GDP) which is one of the indicators that boost the economy. However, some micro-economic variables have been known to influence the Gross Domestic Product. In this research, the Gross Domestic Product per capital of Nigeria from 1989 to 2019 was studied as a function of money supply, foreign direct investment, unemployment and non-oil export. The ordinary least squares estimator and Bayesian approach were adopted to estimate the coefficients of the model. Normal, Gamma, Jeffrey and Uniform priors were considered. The Bayesian estimator with normal prior produced the most efficient estimator of the model coefficients. Prior sensitivity test was carried out and it is discovered that the Bayesian estimator with Jeffrey prior is less sensitive to change in hyper parameters.