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Activity Number: 653 - Advances in Bayesian Nonparametric Modeling and Computation for Complex Data
Type: Topic Contributed
Date/Time: Thursday, August 2, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #328708 Presentation
Title: Recursive Bayesian Predictive Distributions
Author(s): Stephen Walker*
Keywords: Copula; nonparametric Bayes

A Bayesian framework is attractive in the context of prediction, but a fast re- cursive 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 paper 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 non- parametric 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.

Authors who are presenting talks have a * after their name.

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