Date of Award

Fall 11-28-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Stephen Becker

Second Advisor

Jem Corcoran

Third Advisor

Matthew Keller

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Abstract

Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood estimation of such models involves computationally expensive operations on large, dense, and unstructured matrices of high rank. As a result, standard estimation procedures relying on direct matrix methods become prohibitively expensive as sample sizes increase. We propose a novel estimation procedure that uses the Lanczos process and stochastic Lanczos quadrature to approximate the likelihood for an initial choice of parameter values. Then, by identifying the variance components parameter space with a family of shifted linear systems, we are able to exploit the Krylov subspace shift-invariance property to efficiently compute the likelihood for all additional parameter values of interest in linear time. Numerical experiments using simulated data demonstrate increased performance relative to conventional methods with little loss of accuracy.

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