Sequential Inference for Nonlinear Models using Slice Variables

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