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Bayesian estimation of a phenotype network structure using reversible jump Markov chain Monte Carlo

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thesis
posted on 15.11.2021, 09:42 by Woods, Lisa

In this thesis we aim to estimate the unknown phenotype network structure existing among multiple interacting quantitative traits, assuming the genetic architecture is known.  We begin by taking a frequentist approach and implement a score-based greedy hill-climbing search strategy using AICc to estimate an unknown phenotype network structure. This approach was inconsistent and overfitting was common, so we then propose a Bayesian approach that extends on the reversible jump Markov chain Monte Carlo algorithm. Our approach makes use of maximum likelihood estimates in the chain, so we have an efficient sampler using well-tuned proposal distributions. The common approach is to assume uniform priors over all network structures; however, we introduce a prior on the number of edges in the phenotype network structure, which prefers simple models with fewer directed edges. We determine that the relationship between the prior penalty and the joint posterior probability of the true model is not monotonic, there is some interplay between the two.  Simulation studies were carried out and our approach is also applied to a published data set. It is determined that larger trait-to-trait effects are required to recover the phenotype network structure; however, mixing is generally slow, a common occurrence with reversible jump Markov chain Monte Carlo methods. We propose the use of a double step to combine two steps that alter the phenotype network structure. This proposes larger steps than the traditional birth and death move types, possibly changing the dimension of the model by more than one. This double step helped the sampler move between different phenotype network structures in simulated data sets.

History

Copyright Date

01/01/2015

Date of Award

01/01/2015

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Statistics and Operations Research

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

ANZSRC Type Of Activity code

3 APPLIED RESEARCH

Victoria University of Wellington Item Type

Awarded Doctoral Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research

Advisors

Sibanda, Nokuthaba; Arnold, Richard