Computational Methods for the Fitting of Factor Analytic Linear Mixed Models with Applications to Plant Variety Trials

This thesis is concerned with the analysis of plant breeding trials, which involve more data every year, and the addition of genomic information has made these analyses far more computationally demanding. As a result new methods are needed to overcome these challenges and allow these analyses to take place in reasonable time frames; this thesis investigates new algorithms to achieve this. To perform the analyses linear mixed models are ?tted by residual maximum likelihood (REML), using the Average Information (AI) algorithm. The AI algorithm is used as it reduces the computation involved in maximising the residual likelihood, as well as its ability to exploit sparsity and handle a vast range of different variance structures for the random and residual effects. The two most computationally demanding steps are the Cholesky Factorization (CF) of the sum of squares and cross-products matrix, as well as the calculation of the Sparse Inverse Subset (SIS). Various methods from computer science literature in conjunction with novel formulations to perform these steps are described and compared.