Bayesian Analysis of Gene Expression Data (Statistics in Practice).pdf


Bani K. Mallick,
Texas A&M University, USA
David Lee Gold,
University at Buffalo, The State University of New York, USA
and
Veerabhadran Baladandayuthapani,
University of Texas MD Anderson Cancer Center, USA


Table of Notation xi
1 Bioinformatics and Gene Expression Experiments 1
1.1 Introduction 1
1.2 About This Book 3
2 Gene Expression Data: Basic Biology and Experiments 5
2.1 Background Biology 5
2.1.1 DNA Structures and Transcription 6
2.2 Gene Expression Microarray Experiments 9
2.2.1 Microarray Designs 11
2.2.2 Work Flow 11
2.2.3 Data Cleaning 15
3 Bayesian Linear Models for Gene Expression 21
3.1 Introduction 21
3.2 Bayesian Analysis of a Linear Model 22
3.2.1 Analysis via Conjugate Priors 23
3.2.2 Bayesian Variable Selection 25
3.2.3 Model Selection Priors 26
3.2.4 Priors on Regression Coefficients 27
3.2.5 Sparsity Priors 29
3.3 Bayesian Linear Models for Differential Expression 30
3.3.1 Relevant Work 32
3.4 Bayesian ANOVA for Gene Selection 34
3.4.1 The Basic Bayesian ANOVA Model 35
3.4.2 Differential Expression via Model Selection 36
3.5 Robust ANOVA model with Mixtures of Singular Distributions 38
3.6 Case Study 40
3.7 Accounting for Nuisance Effects 43
3.8 Summary and Further Reading 49
4 Bayesian Multiple Testing and False Discovery Rate Analysis 51
4.1 Introduction to Multiple Testing 51
viii CONTENTS
4.2 False Discovery Rate Analysis 53
4.2.1 Theoretical Developments 53
4.2.2 FDR Analysis with Gene Expression Arrays 57
4.3 Bayesian False Discovery Rate Analysis 60
4.3.1 Theoretical Developments 60
4.4 Bayesian Estimation of FDR 61
4.5 FDR and Decision Theory 65
4.6 FDR and bFDR Summary 65
5 Bayesian Classification for Microarray Data 69
5.1 Introduction 69
5.2 Classification and Discriminant Rules 71
5.3 Bayesian Discriminant Analysis 72
5.4 Bayesian Regression Based Approaches to Classification 74
5.4.1 Bayesian Analysis of Generalized Linear Models 75
5.4.2 Link Functions 75
5.4.3 GLM using Latent Processes 76
5.4.4 Priors and Computation 76
5.4.5 Bayesian Probit Regression using Auxiliary Variables 77
5.5 Bayesian Nonlinear Classification 79
5.5.1 Classification using Interactions 79
5.5.2 Classification using Kernel Methods 82
5.6 Prediction and Model Choice 84
5.7 Examples 85
5.8 Discussion 87
6 Bayesian Hypothesis Inference for Gene Classes 89
6.1 Interpreting Microarray Results 89
6.2 Gene Classes 90
6.2.1 Enrichment Analysis 92
6.3 Bayesian Enrichment Analysis 94
6.4 Multivariate Gene Class Detection 95
6.4.1 Extending the Bayesian ANOVA Model 98
6.4.2 Bayesian Decomposition 105
6.5 Summary 107
7 Unsupervised Classification and Bayesian Clustering 109
7.1 Introduction to Bayesian Clustering for Gene Expression Data 109
7.2 Hierarchical Clustering 111
7.3 K-Means Clustering 112
7.4 Model-Based Clustering 114
7.5 Model-Based Agglomerative Hierarchical Clustering 115
7.6 Bayesian Clustering 116
7.7 Principal Components 117
7.8 Mixture Modeling 119
CONTENTS ix
7.8.1 Label Switching 124
7.9 Clustering Using Dirichlet Process Prior 126
7.9.1 Infinite Mixture of Gaussian Distributions 131
8 Bayesian Graphical Models 137
8.1 Introduction 137
8.2 Probabilistic Graphical Models 138
8.3 Bayesian Networks 138
8.4 Inference for Network Models 141
8.4.1 Multinomial-Dirichlet Model 143
8.4.2 Gaussian Model 145
8.4.3 Model Search 146
8.4.4 Example 148
9 Advanced Topics 151
9.1 Introduction 151
9.2 Analysis of Time Course Gene Expression Data 151
9.2.1 Gene Selection 152
9.2.2 Functional Clustering 153
9.2.3 Dynamic Bayesian Networks 155
9.3 Survival Prediction Using Gene Expression Data 155
9.3.1 Gene Selection for Time-to-Event Outcomes 156
9.3.2 Weibull Regression Model 156
9.3.3 Proportional Hazards Model 157
9.3.4 Accelerated Failure Time Model 158
Appendix A: Basics of Bayesian Modeling 159
A.1 Basics 159
A.1.1 The General Representation Theorem 160
A.1.2 Bayes’ Theorem 161
A.1.3 Models Based on Partial Exchangeability 162
A.1.4 Modeling with Predictors 162
A.1.5 Prior Distributions 163
A.1.6 Decision Theory and Posterior and Predictive Inferences 165
A.1.7 Predictive Distributions 168
A.1.8 Examples 168
A.2 Bayesian Model Choice 172
A.3 Hierarchical Modeling 175
A.4 Bayesian Mixture Modeling 181
A.5 Bayesian Model Averaging 183
Appendix B: Bayesian Computation Tools 185
B.1 Overview 185
B.2 Large-Sample Posterior Approximations 186
B.2.1 The Bayesian Central Limit Theorem 186
x CONTENTS
B.2.2 Laplace’s Method 188
B.3 Monte Carlo Integration 191
B.4 Importance Sampling 192
B.5 Rejection Sampling 193
B.6 Gibbs Sampling 195
B.7 The Metropolis Algorithm and Metropolis–Hastings 198
B.8 Advanced Computational Methods 202
B.8.1 Block MCMC 203
B.8.2 Truncated Posterior Spaces 204
B.8.3 Latent Variables and the Auto-Probit Model 204
B.8.4 Bayesian Simultaneous Credible Envelopes 205
B.8.5 Proposal Updating 206
B.9 Posterior Convergence Diagnostics 207
B.10 MCMC Convergence and the Proposal 208
B.10.1 Graphical Checks for MCMC Methods 211
B.10.2 Convergence Statistics 212
B.10.3 MCMC in High-throughput Analysis 213
B.11 Summary 214