- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Nonparametric Bayesian models for Markov jump processes
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Nonparametric Bayesian models for Markov jump processes Saeedi, Ardavan
Abstract
Markov jump processes (MJPs) have been used as models in various fields such as disease progression, phylogenetic trees, and communication networks. The main motivation behind this thesis is the application of MJPs to data modeled as having complex latent structure. In this thesis we propose a nonparametric prior, the gamma-exponential process (GEP), over MJPs. Nonparametric Bayesian models have recently attracted much attention in the statistics community, due to their flexibility, adaptability, and usefulness in analyzing complex real world datasets. The GEP is a prior over infinite rate matrices which characterize an MJP; this prior can be used in Bayesian models where an MJP is imposed on the data but the number of states of the MJP is unknown in advance. We show that the GEP model we propose has some attractive properties such as conjugacy and simple closed-form predictive distributions. We also introduce the hierarchical version of the GEP model; sharing statistical strength can be considered as the main motivation behind the hierarchical model. We show that our hierarchical model admits efficient inference algorithms. We introduce two inference algorithms: 1) a “basic” particle Markov chain Monte Carlo (PMCMC) algorithm which is an MCMC algorithm with sequences proposed by a sequential Monte Carlo (SMC) algorithm; 2) a modified version of this PMCPC algorithm with an “improved” SMC proposal. Finally, we demonstrate the algorithms on the problems of estimating disease progression in multiple sclerosis and RNA evolutionary modeling. In both domains, we found that our model outperformed the standard rate matrix estimation approach.
Item Metadata
Title |
Nonparametric Bayesian models for Markov jump processes
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
2012
|
Description |
Markov jump processes (MJPs) have been used as models in various fields such as
disease progression, phylogenetic trees, and communication networks. The main
motivation behind this thesis is the application of MJPs to data modeled as having
complex latent structure. In this thesis we propose a nonparametric prior, the
gamma-exponential process (GEP), over MJPs. Nonparametric Bayesian models
have recently attracted much attention in the statistics community, due to their flexibility,
adaptability, and usefulness in analyzing complex real world datasets. The
GEP is a prior over infinite rate matrices which characterize an MJP; this prior can
be used in Bayesian models where an MJP is imposed on the data but the number of
states of the MJP is unknown in advance. We show that the GEP model we propose
has some attractive properties such as conjugacy and simple closed-form predictive
distributions. We also introduce the hierarchical version of the GEP model;
sharing statistical strength can be considered as the main motivation behind the hierarchical
model. We show that our hierarchical model admits efficient inference
algorithms. We introduce two inference algorithms: 1) a “basic” particle Markov
chain Monte Carlo (PMCMC) algorithm which is an MCMC algorithm with sequences
proposed by a sequential Monte Carlo (SMC) algorithm; 2) a modified
version of this PMCPC algorithm with an “improved” SMC proposal. Finally, we
demonstrate the algorithms on the problems of estimating disease progression in
multiple sclerosis and RNA evolutionary modeling. In both domains, we found
that our model outperformed the standard rate matrix estimation approach.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2012-08-17
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0073015
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
2012-11
|
Campus | |
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International