Quantitative trait loci (QTL) mapping is one of the applications of statistics in genetics.This dissertation focuses two problems on QTL mapping which include a newpermutation method used to find the thresholds for the shrinkage Bayesian estimation ofquantitative trait loci parameters and three algorithms of handling the missing genotype
problems in multiple QTL mapping under the generalized linear mixed model framework.In addition, this dissertation includes a review on Bayesian statistics and somedata analyses using Markov chain Monte Carlo (MCMC).
Chapter 2 is a review of the Bayesian statistics and some data analyses usingMCMC. It includes almost all the aspects of Bayesian statistics such as Bayes' theorem, prior and posterior distributions, Bayesian inference, and Markov chain Monte Carlo (MCMC) algorithms.
In Chapter 3, a new way to conduct the permutation test under the Shrinkage Bayesian method is developed. Permutation test is the most frequently used method for statistical test for QTL mapping. And it was applied on the QTL mapping based on the Bayesian approach. While using the traditional permutation test to get the thresholds for QTL mapping from the MCMC algorithms in the Bayesian models is
quite time-consuming, a new way to permute the samples from the MCMC algorithmsis performed in Chapter 3. Empirical power analysis is done to test the method through the simulations.
Generalized linear mixed model has been applied to analyze the discrete traits. Research on handling the missing genotype problems in multiple QTL mapping under the generalized linear mixed model framework is presented in Chapter 4. Three algorithms were proposed: (1) expectation algorithm, (2) overdispersion model algorithm and (3)
mixture model algorithm.