Bayesian Regression Estimation with Balanced Weighted Precision Loss Function: Cross-Sectional-Qualitative Studies

Abstract

The main aim of this study is to derive the alternative risk and loss function for Bayesian paradigm. Bayesian Decision making is an integral part of Bayesian infer-ence which had for long overshadowed due to the adoption of frequentist performance metric, and Bayesian inference is proba-bilistic in nature, treating it in classical paradigm would lead to poor performances. This study seeks to examine critically and introduce weight which eventually makes Bayesian estimates compare favourably well with classical estimates. Material and Methods: Balanced weighted precision loss function was adopted and described; it is an extraction of precision of estimates from balanced loss function which ordinarily combined goodness of fit and precision of estimates. The goodness of fit criterion measures the quality of data while the precision of estimates measures the quality of inferences, combining the two criteria may lead to loss of information as each criterion has its specific role in both clas-sical and Bayesian paradigms. Results: Weighted quadratic loss to measure the precision of estimates of Posterior mean and Bayes estimate were constructed as a standard metric. The study established the estimation characteristics under weighted quadrat-ic loss function which makes Bayesian inference compare favour-ably well with other estimators. Conclusion: It is therefore rec-ommended that weighted quadratic loss function of assessment criteria of both posterior mean and Bayes estimates is of im-portance for correct comparison.