Monte Carlo-Based Identification Strategies for State-Space Models

0505335 - ÚTIA 2020 RIV CZ eng D - Thesis
Papež, Milan
Monte Carlo-Based Identification Strategies for State-Space Models.
Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií. Defended: Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií. 16.5.2019. - Brno: Vysoké učení technické v Brně, 2019. 224 s.
R&D Projects: GA ČR(CZ) GA18-15970S
Institutional support: RVO:67985556
Keywords : sequential Monte Carlo * particle Markov chain Monte Carlo * nonlinear and non-Gaussian state-space models * transfer learning
OECD category: Statistics and probability
http://library.utia.cas.cz/separaty/2019/AS/papez-0505335.pdf

State-space models are immensely useful in various areas of science and engineering. Their attractiveness results mainly from the fact that they provide a generic tool for describing a wide range of real-world dynamical systems. However, owing to their generality, the associated state and parameter inference objectives are analytically intractable in most practical cases. The present thesis considers two particularly important classes of nonlinear and non-Gaussian state-space models: conditionally conjugate state-space models and jump Markov nonlinear models. A key feature of these models lies in that---despite their intractability---they comprise a tractable substructure. The intractable part requires us to utilize approximate techniques. Monte Carlo computational methods constitute a theoretically and practically well-established tool to address this problem. The advantage of these models is that the tractable part can be exploited to increase the efficiency of Monte Carlo methods by resorting to the Rao-Blackwellization. Specifically, this thesis proposes two Rao-Blackwellized particle filters for identification of either static or time-varying parameters in conditionally conjugate state-space models. Furthermore, this work adopts recent particle Markov chain Monte Carlo methodology to design Rao-Blackwellized particle Gibbs kernels for state smoothing in jump Markov nonlinear models. The kernels are then used to facilitate maximum likelihood parameter inference in the considered models. The resulting experiments demonstrate that the proposed algorithms outperform related techniques in terms of the estimation precision and computational time.
Permanent Link: http://hdl.handle.net/11104/0296952