V
2.5 Priors, Posterior and Simulation Scheme................ 21
2.6 Applications................................ 25
2.6.1 A Simulated Dataset....................... 25
2.6.2 A Phase III Clinical Trial of Retinoid Isotretinoin....... 27
2.7 Discussion................................. 30
3 Dirichlet Process Mixture Models for Discrete Human Data in Phage
Display Model 37
3.1 Overview.................................. 38
3.2 Background................................ 41
3.2.1 Dirichlet Distribution....................... 41
3.2.2 Dirichlet Process and Dirichlet Process Mixture Model .... 42
3.2.3 Gibbs Sampling Scheme for DPM................ 46
3.2.4 Example of Application of DPM in Density Estimation .... 52
3.3 Data.................................... 57
3.4 Model................................... 60
3.4.1 A Semi-parametric Mixture of Poisson Model ......... 60
3.4.2 Posterior Simulation....................... 63
3.5 Selecting Significant Tripeptide-Tissue Pairs.............. 66
3.6 A Simulation Study............................ 69
3.7 Results................................... 72
3.8 Discussion................................. 78
4 Borrowing Strength with Hierarchical Models over Non-Exchangeable
Subpopulations 81
4.1 Outline................................... 81
4.2 Data.................................... 83
4.3 Non-Exchangeable Product Partition Model.............. 84
4.3.1 Model Definition......................... 84
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