A study of Population MCMC for estimating Bayes Factors over nonlinear ODE models

Calderhead, Ben (2008) A study of Population MCMC for estimating Bayes Factors over nonlinear ODE models. MSc(R) thesis, University of Glasgow.

Abstract

Higher resolution biological data is now becoming available in ever greater quantities, allowing the complex behaviour of fundamental biological processes to be studied in much more detail. The area of Systems Biology is in desperate need of methods for inferring the most likely topology of the underlying genetic networks from this oftentimes noisy and poorly sampled data, to support the construction and testing of new model hypotheses. Towards that end, Bayesian methodology provides an ideal framework for tackling such challenges, and in particular offers a means of objectively comparing competing plausible models through the estimation of Bayes factors.

There are, however, formidable obstacles which must be overcome to allow model inference using Bayes factors to be of practical use. Many important biological processes may be most accurately represented using nonlinear models based on systems of ordinary differential equations (ODEs), however parameter inference over these models often produces correspondingly nonlinear posterior distributions, which are very challenging to sample from, often resulting in biased
marginal likelihood estimates with large variances. Such problems are commonly encountered when modelling circardian rhythms, which exhibit highly nonlinear oscillatory dynamics and play a central role in the overall functioning of most
organisms. In this thesis I investigate tools for calculating Bayes factors to distinguish between ODE-based Goodwin oscillator models of varying complexity, which form the basic building blocks for describing this ubiquitous circadian behaviour.

The main result in Chapter 3 of this thesis demonstrates how Population Markov Chain Monte Carlo may be employed in conjunction with thermodynamic integration methods to estimate Bayes factors which may accurately distinguish
between two nonlinear oscillator models of varying complexity, given noisy experimental data generated from each of the models. In addition, it is shown how alternative methods may fail drastically in this setting, in particular harmonic mean based estimates. Suggestions are given regarding the optimal temperature schedule which should be employed for Population MCMC, and several ideas for future research extending this work are also discussed.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• Keywords: Bayesian inference, MCMC methods, systems biology, marginal likelihood, model comparison, ODEs, oscillatory biological systems
• Subjects: Q Science > QA Mathematics; Q Science > Q Science (General)
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Girolami, Prof Mark
• Date of Award: 2008
• Depositing User: Mr Ben Calderhead
• Unique ID: glathesis:2008-304
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 20 Jun 2008
• Last Modified: 10 Dec 2012 13:17
• URI: https://theses.gla.ac.uk/id/eprint/304