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Non-Linear and Non-Gaussian State Space Models

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Bayesian Inference of State Space Models

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Abstract

This chapter discusses estimation for non-linear and non-Gaussian state space methods. We start by defining conditionally Gaussian and more general non-Gaussian and non-linear state space models. The text reviews some classes of the many possibilities of non-Gaussian models. In particular, dynamic generalised linear models (DGLM) are discussed aimed at categorical time series, count data, data for positive-valued time series, continuous proportions and so forth. Other models such as bearings-only tracking and stochastic volatility models are also considered. The first attempts to model non-Gaussian state space models includes the power local level models and these are described for historical and pedagogical purposes. The chapter moves on discussing approximate inference such as the extended Kalman filter and the unscented Kalman filter. Sequential Monte Carlo methods are reviewed and some illustrative examples are presented. Markov chain Monte Carlo is discussed for the class of DGLMs, and the chapter concludes by considering dynamic survival modelling.

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  1. School of Mathematics, University of Sheffield, Sheffield, UK

    Kostas Triantafyllopoulos

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Triantafyllopoulos, K. (2021). Non-Linear and Non-Gaussian State Space Models. In: Bayesian Inference of State Space Models. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-76124-0_6

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