Stochastic Lanczos Likelihood Estimation of Genomic Variance Components

Graduate Thesis Or Dissertation

Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/x059c761r

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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