A Note on Modal Filtering for Conditionally Gaussian Dynamic Nonlinear Models

E. Gutiérrez-Peña

IIMAS-UNAM, Mexico

Abstract. For Gaussian dynamic linear models all the distributions involved in the analysis are normal, and hence characterized by their first two moments only. When a nonlinear term appears in the observation equation, however, means and variances may no longer provide adequate summaries of the posterior distributions of the parameters, so alternative techniques are required. In this paper we review and extend a modal filtering algorithm of Fahrmeir and Kaufmann (1991). A new feature of our algorithm is the ability to cope with multimodal posterior distributions arising from some nonlinear systems.

Key words: Bayesian inference, dynamic models, Kalman filter, posterior mode estimation.