In the practice of statistical modeling, it is often desirable to have an accurate predictive model. Modern data sets usually have a large number of predictors. For example, DNA microarray gene expression data usually have the characteristics of fewer observations and larger number of variables. Hence parsimony is especially an important issue. Best-subset selection is a conventional method of variable selection. Due to the large number of variables with relatively small sample size and severe collinearity among the variables, standard statistical methods for selecting relevant variables often face difficulties.;The second part of the thesis proposes a Bayesian stochastic variable selection approach for gene selection based on a probit regression model with a generalized singular g-prior distribution for regression coefficients. Using simulation-based MCMC methods for simulating parameters from the posterior distribution, an efficient and dependable algorithm is implemented. It is also shown that this algorithm is robust to the choice of initial values, and produces posterior probabilities of related genes for biological interpretation. The performance of the proposed approach is compared with other popular methods in gene selection and classification via the well known colon cancer and leukemia data sets in microarray literature.;In the third part of the thesis, we propose a Bayesian stochastic search variable selection approach for multi-class classification, which can identify relevant genes by assessing sets of genes jointly. We consider a multinomial probit model with a generalized g-prior for the regression coefficients. An efficient algorithm using simulation-based MCMC methods are developed for simulating parameters from the posterior distribution. This algorithm is robust to the choice of initial value, and produces posterior probabilities of relevant genes for biological interpretation. We demonstrate the performance of the approach with two well- known gene expression profiling data: leukemia data and lymphoma data. Compared with other classification approaches, our approach selects smaller numbers of relevant genes and obtains competitive classification accuracy based on obtained results.;The last part of the thesis is about the further research, which presents a stochastic variable selection approach with different two-level hierarchical prior distributions. These priors can be used as a sparsity-enforcing mechanism to perform gene selection for classification. Using simulation-based MCMC methods for simulating parameters from the posterior distribution, an efficient algorithm can be developed and implemented.
展开▼
