Bayesian Analysis of Gene Expression Data

1 Bioinformatics and Gene Expression Experiments.

1.1 Introduction.

1.2 About This Book.

2 Basic Biology.

2.1 Background.

2.1.1 DNA Structures and Transcription.

2.2 Gene Expression Microarray Experiments.

3 Bayesian Linear Models for Gene Expression.

3.1 Introduction.

3.2 Bayesian Analysis of a Linear Model.

3.3 Bayesian Linear Models for Differential Expression.

3.4 Bayesian ANOVA for Gene Selection.

3.5 Robust ANOVA model with Mixtures of Singular Distributions.

3.6 Case Study.

3.7 Accounting for Nuisance Effects.

3.8 Summary and Further Reading.

4 Bayesian Multiple Testing and False Discovery Rate Analysis.

4.1 Introduction to Multiple Testing.

4.2 False Discovery Rate Analysis.

4.3 Bayesian False Discovery Rate Analysis.

4.4 Bayesian Estimation of FDR.

4.5 FDR and Decision Theory.

4.6 FDR and bFDR Summary.

5 Bayesian Classification for Microarray Data.

5.1 Introduction.

5.2 Classification and Discriminant Rules.

5.3 Bayesian Discriminant Analysis.

5.4 Bayesian Regression Based Approaches to Classification.

5.5 Bayesian Nonlinear Classification.

5.6 Prediction and Model Choice.

5.7 Examples.

5.8 Discussion.

6 Bayesian Hypothesis Inference for Gene Classes.

6.1 Interpreting Microarray Results.

6.2 Gene Classes.

6.3 Bayesian Enrichment Analysis.

6.4 Multivariate Gene Class Detection.

6.5 Summary.

7 Unsupervised Classification and Bayesian Clustering.

7.1 Introduction to Bayesian Clustering for Gene Expression Data.

7.2 Hierarchical Clustering.

7.3 K-Means Clustering.

7.4 Model-Based Clustering.

7.5 Model-Based Agglomerative Hierarchical Clustering.

7.6 Bayesian Clustering.

7.7 Principal Components.

7.8 Mixture Modeling.

7.8.1 Label Switching.

7.9 Clustering Using Dirichlet Process Prior.

7.9.1 Infinite Mixture of Gaussian Distributions.

8 Bayesian Graphical Models.

8.1 Introduction.

8.2 Probabilistic Graphical Models.

8.3 Bayesian Networks.

8.4 Inference for Network Models.

9 Advanced Topics.

9.1 Introduction.

9.2 Analysis of Time Course Gene Expression Data.

9.3 Survival Prediction Using Gene Expression Data.

Appendix A: Basics of Bayesian Modeling.

A.1 Basics.

A.1.1 The General Representation Theorem.

A.1.2 Bayes’ Theorem.

A.1.3 Models Based on Partial Exchangeability.

A.1.4 Modeling with Predictors.

A.1.5 Prior Distributions.

A.1.6 Decision Theory and Posterior and Predictive Inferences.

A.1.7 Predictive Distributions.

A.1.8 Examples.

A.2 Bayesian Model Choice.

A.3 Hierarchical Modeling.

A.4 Bayesian Mixture Modeling.

A.5 Bayesian Model Averaging.

Appendix B: Bayesian Computation Tools.

B.1 Overview.

B.2 Large-Sample Posterior Approximations.

B.2.1 The Bayesian Central Limit Theorem.

B.2.2 Laplace’s Method.

B.3 Monte Carlo Integration.

B.4 Importance Sampling.

B.5 Rejection Sampling.

B.6 Gibbs Sampling.

B.7 The Metropolis Algorithm and Metropolis–Hastings.

B.8 Advanced Computational Methods.

B.8.1 Block MCMC.

B.8.2 Truncated Posterior Spaces.

B.8.3 Latent Variables and the Auto-Probit Model.

B.8.4 Bayesian Simultaneous Credible Envelopes.

B.8.5 Proposal Updating.

B.9 Posterior Convergence Diagnostics.

B.10 MCMC Convergence and the Proposal.

B.10.1 Graphical Checks for MCMC Methods.

B.10.2 Convergence Statistics.

B.10.3 MCMC in High-Throughput Analysis.

B.11 Summary.

References.

Index.