Chen, Sida (2021) Bayesian inference for nonparametric hidden Markov models with applications to physiological data. PhD thesis, University of Warwick.

Preview

PDF WRAP_Theses_Chen_2021.pdf - Submitted Version - Requires a PDF viewer. Download (1550Kb) | Preview

Request Changes to record.

Abstract

This thesis develops new nonparametric Bayesian hidden Markov models (HMM) and estimation methods that address some of the challenges and limitations of existing nonparametric approaches. In chapter 2, we introduce for the first time a fully Bayesian method for inference in spline-based HMMs where the number of states may be unknown along with other model parameters including the knot configuration of the B-splines. Regarding the latter, we propose the use of a transdimensional Markov chain Monte Carlo (MCMC) algorithm, while model selection regarding the number of states can be achieved based on the estimated marginal likelihood. Our methodology compares favourably with existing competing methods in terms of estimation accuracy, stability and efficiency. We then extend the splinebased HMM proposed in chapter 2 to develop a novel hierarchical conditional HMM approach, which allows us to analyse the specific state of an HMM at a finer level with another sub-HMM, achieving inferences that are otherwise not possible with a single HMM. We apply the proposed method to human activity data from wearable devices where we can jointly identify and characterise sleep periods, an area of interest to sleep and circadian biology research. In the last part of the thesis, we exploit the strength of the hierarchical Dirichlet process and a suitable integration with HMMs to develop new Bayesian nonparametic multivariate HMMs. The resulting models allow for flexible yet parsimonious modelling of the emission distributions and automatic learning of the state cardinality, generalising existing models to offer greater modelling flexibility. We develop novel MCMC methods which combine the slice sampling technique and a dynamic programming algorithm for exact and efficient posterior inference. Finally, we apply our proposed models to motion and heart rate data collected from the Apple watch for learning human sleep dynamics in an unsupervised context.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Bayesian statistical decision theory, Markov processes, Monte Carlo method, Activity trackers (Wearable technology) -- Data processing
Official Date:	October 2021
Dates:	Date Event October 2021 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Finkenstädt, Bärbel
Sponsors:	Association of British Chinese Professors
Format of File:	pdf
Extent:	xii, 154 leaves : illustrations
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads