A Bayesian Approach for Predicting With Polynomial Regression of Unknown Degree

Abstract

This article compares three methods for computing the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high-density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures is illustrated with simulations and some known engineering data.