Determination of Quantile Range of Optimal Hyperparameters Using Bayesian Estimation

Abstract

Bayesian estimations have the advantages of taking into account the uncertainty of all parameter estimates which allows virtually the use of vague priors. This study focused on determining the quantile range at which optimal hyperparameter of normally distributed data with vague information could be obtained in Bayesian estimation of linear regression models. A Monte Carlo simulation approach was used to generate a sample size of 200 data-set. Observation precisions and posterior precisions were estimated from the regression output to determine the posterior means estimate for each model to derive the new dependent variables. The variances were divided into 10 equal parts to obtain the hyperparameters of the prior distribution. Average absolute deviation for model selection was used to validate the adequacy of each model. The study revealed the optimal hyperparameters located at 5th and 7th deciles. The research simplified the process of selecting the hyperparameters of prior distribution from the data with vague information in empirical Bayesian inferences.
 Keywords: Optimal Hyperparameters; Quantile Ranges; Bayesian Estimation; Vague prior