Sequential Inference for Nonlinear Models using Slice Variables

35 Pages Posted: 21 Nov 2009  

Michael S. Johannes

Columbia Business School - Finance and Economics

Nick Polson

University of Chicago - Booth School of Business

Seung M. Yae

University of Chicago - Booth School of Business

Date Written: November 19, 2009

Abstract

This paper develops particle-based methods for sequential inference in nonlinear models. Sequential inference is notoriously difficult in nonlinear state space models. To overcome this, we use auxiliary state variables to slice out nonlinearities where appropriate. This induces a Fixed-dimension conditional sufficient statistics and, given these, we adapt existing particle learning algorithms to update posterior beliefs about states and parameters. We provide three illustrations. First, a dynamic exponential model with Gaussian errors. Second, a stochastic growth model with nonlinear state evolution and t-distributed errors. Finally, a bivariate radar tracking problem which was originally analyzed in the nonlinear Monte Carlo Filtering literature. In all cases, we illustrate the efficiency of our methodology.

Keywords: Monte Carlo, Particle Filtering, Particle Learning, Nonlinear State Space Model, Slice Variable

JEL Classification: C1, C11, C15

Suggested Citation

Johannes, Michael S. and Polson, Nick and Yae, Seung M., Sequential Inference for Nonlinear Models using Slice Variables (November 19, 2009). Available at SSRN: https://ssrn.com/abstract=1509782 or http://dx.doi.org/10.2139/ssrn.1509782

Michael Slater Johannes

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States

Nick Polson (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

Seung Min Yae

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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