OBTAINING BAYESIAN POSTERIOR ESTIMATES USING QUANTILES NORMAL HYPERPARAMETERS AS PRIOR

Abstract

This research work focused on obtaining Bayesian posterior estimates using quantiles normal hyperparameters as prior. This is with a view to obtain prior estimates using quantiles of the confidence interval of the Ordinary Least Square (OLS) estimate and determine the adequacy of the models in order to identify the best. The data used was a secondary data, collected from the Ministry of Land and Physical Planning, Osogbo, Osun State. The Confidence Interval (CI) was divided into 100 equal parts to give 99 grid points and each grid point is taken as the hyperparameter of the prior distributions. The values of the prior hyperparameters are chosen to reflect the prior information. The posterior mean is the estimate of the regression coefficient  0 -  2 and for each of the 99 models, we obtain the Mean Absolute Deviation (MAD) and choose the model with the least MAD as the corresponding optimal hyperparameter. The least MAD corresponds to the 47th model 214936.629338.4619972.9126ˆXXY which is better than OLS; even though there are other models with lower MAD than that of OLS estimate.