Differential geometric MCMC methods and applications

Calderhead, Ben (2011) Differential geometric MCMC methods and applications. PhD thesis, University of Glasgow.

Abstract

This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure. The performance of these Riemannian manifold Markov chain Monte Carlo algorithms is rigorously assessed by performing Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Inference, Markov chain Monte Carlo, Bayesian statistics, Hamiltonian Monte Carlo, Riemannian manifold, Langevin diffusion
• Subjects: Q Science > QC Physics; Q Science > QA Mathematics; Q Science > Q Science (General)
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Mark, Prof. Girolami
• Date of Award: 2011
• Depositing User: Mr Ben Calderhead
• Unique ID: glathesis:2011-3258
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 08 Mar 2012
• Last Modified: 10 Dec 2012 14:05
• URI: https://theses.gla.ac.uk/id/eprint/3258