Classical Regression Estimation Versus Bayesian Regression Estimation: A Simulation-based Analysis of Predictive Performance
Thomas Adidaumbe Ugbe *
Department of Statistics, University of Calabar, Cross River State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study uses a simulated macroeconomic dataset with 100 observations to compare Ordinary Least Squares (OLS) regression versus Bayesian regression for GDP modelling. Investment, consumption, and government spending are included in the model definition as important explanatory variables. Under stringent distributional assumptions, OLS, which is based on the traditional frequentist paradigm, yields parameter estimates that are solely obtained from the observed sample. In contrast, Bayesian regression produces posterior estimates by integrating prior distributions with the likelihood, providing a probabilistic description of parameter uncertainty. The methodological significance of prior specification was highlighted by the unstable inferences obtained from initial Bayesian estimation using weakly informative priors. However, posterior convergence and predictive alignment with OLS findings were significantly enhanced by the addition of sophisticated, commercially viable priors. While Bayesian regression provided wider credible intervals reflecting uncertainty, OLS produced more accurate (narrower) predicted intervals. The results confirm that Bayesian regression is a rigorous and reliable substitute for OLS when backed by well-informed priors, especially in situations with sparse data or ambiguous model assumptions.
Keywords: Informed priors, mean square error, multicollinearity, predictive interval, markov chain monte carlo