Polynomial Regression from a Bayesian Approach

Abstract The problem of prediction with a normal error polynomial regression model with uncertainty about the degree is considered. Priors incorporating this uncertainty are used; posteriors are explicitly derived for natural conjugate priors and shown to be consistent. The optimal predictor is shown to be a function of the marginal probabilities of the degree and of the mean values of the distribution of the coefficients when the loss in using p(x) (of degree d) to predict while the true regression curve is t(x) (of degree δ) is