A new approach to adaptive particle filters for joint state and parameter estimation in hidden Markov models
Abstract/Contents
- Abstract
- The landmark paper by Gordon, Salmond and Smith \cite{GSS93} launched the development of sequential Monte Carlo (SMC), also called particle filters, for the estimation of latent states in hidden Markov models (HMM). Liu \cite{Liu01} contains a collection of the techniques that have been developed since then, with examples of applications in computational biology and engineering, and Chan and Lai \cite{CL12} provide a general theory of particle filters, assuming the model parameters to be pre-specified. This assumption is too restrictive in practice, since the model parameters are usually unknown and also need to be estimated sequentially from the observed data. The obvious approach that treats the parameters as latent states and thereby incorporates them in a larger state vector suffers from severe degeneracy difficulties of the particle filter because the subvector corresponding to the parameters does not undergo Markovian dynamics. Beginning with Liu and West \cite{LW01} and Storvik \cite{Sto02}, there have been many proposals to address this difficulty; see \cite{ADH10}. In particular, Andrieu, Doucet and Holenstein \cite{ADH10} developed the particle MCMC (PMCMC) approach and Chopin, Jacob, and Papaspiliopoulos\cite{CJP12} subsequently introduced the SMC$^2$ method. These two approaches have achieved the state-of-the-art performance. In this thesis, we introduce a new approach to adaptive particle filters for joint parameter and state estimation in HMMs and develop a complete asymptotic theory showing its computational and statistical advantages over previous methods. This approach also provides consistent estimates of (a) the standard errors for the Monte Carlo estimate and (b) mean squared errors of the adaptive particle filter. We accomplish this by combining the theory of particle filters for state estimation in Chan and Lai \cite{CL12} when the parameters are known with that of a novel MCMC scheme using sequential state substitutions for parameter estimation (MCMC-SS) in Lai, Zhu and Chan\cite{LZC19}. Chapter 2 describes our new adaptive particle filter, its computational advantages and how it seamlessly combines the aforementioned two components (a) and (b). Applications to nonlinear state space models in automatic navigation and to HMMs in quantitative finance are given in Chapter 3. Concluding remarks are given in Chapter 4, in which we also provide further discussion of our approach and additional related references in the literature.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Gao, Pengfei |
|---|---|
| Degree supervisor | Lai, T. L |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Hong, Han |
| Thesis advisor | Lu, Ying, 1960- |
| Degree committee member | Hong, Han |
| Degree committee member | Lu, Ying, 1960- |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Pengfei Gao. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Pengfei Gao
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