Microarray is a high throughput technology to measure the gene expression. Analysis of microarray data brings many interesting and challenging problems. This thesis consists three studies related to microarray data. First, we propose a Bayesian model for microarray data and use Bayes Factors to identify differentially expressed genes. Second, we study the cellular differentiation process and proposed a statistical test for detecting early differentiation genes. Third, we further proposed a model-based method for the cellular differentiation problem. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]