Fitting linear mixed models using sparse matrix methods and Lanczos factorization
这篇论文探索并改进了现代统计计算方法，重点应用于遗传学，包括使用稀疏矩阵方法求解线性混合模型、开发PruneDIRECT优化算法，以及研究强迫行为中的母体效应。
The goal of this thesis is to explore, improve and implement some advanced modern computational methods in statistics, focusing on applications in genetics. The thesis has three major directions.First, we study likelihoods for genetics analysis of experimental populations. Here, the maximum likelihood can be viewed as a computational global optimization problem. We introduce a faster optimization algorithm called PruneDIRECT, and explain how it can be parallelized for permutation testing using the Map-Reduce framework. We have implemented PruneDIRECT as an open source R package, and also Software as a Service for cloud infrastructures (QTLaaS).The second part of the thesis focusses on using sparse matrix methods for solving linear mixed models with large correlation matrices. For populations with known pedigrees, we show that the inverse of covariance matrix is sparse. We describe how to use this sparsity to develop a new method to maximize the likelihood and calculate the variance components.In the final part of the thesis we study computational challenges of psychiatric genetics, using only pedigree information. The aim is to investigate existence of maternal effects in obsessive compulsive behavior. We add the maternal effects to the linear mixed model, used in the second part of this thesis, and we describe the computational challenges of working with binary traits.