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.
