On Recursive Bayesian Predictive Distributions

原文摘要

P. Richard Hahna, Ryan Martinb* & Stephen G. Walkerca Booth School of Business, The University of Chicago, Chicago, ILb Department of Statistics, North Carolina State University, NCc Department of Mathematics, University of Texas at Austin, TXCONTACT Ryan Martin rgmarti3@ncsu.edu Department of Statistics, North Carolina State University, NC 27607Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.ABSTRACTA Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive. This article shows that online Bayesian prediction is possible by characterizing the Bayesian predictive update in terms of a bivariate copula, making it unnecessary to pass through the posterior to update the predictive. In standard models, the Bayesian predictive update corresponds to familiar choices of copula but, in nonparametric problems, the appropriate copula may not have a closed-form expression. In such cases, our new perspective suggests a fast recursive approximation to the predictive density, in the spirit of Newton’s predictive recursion algorithm, but without requiring evaluation of normalizing constants. Consistency of the new algorithm is shown, and numerical examples demonstrate its quality performance in finite-samples compared to fully Bayesian and kernel methods. Supplementary materials for this article are available online.

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