Bayesian Analysis of Gene Expression Data (eBook)

Bani Mallick, Department of Statistics, Texas A&M University, USA. Veera Balandandayuthapani, Department of Biostatistics, Anderson Cancer Center, Texas, USA. David L. Gold, Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, The State University of New York, USA.

Table of Notation.

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 SingularDistributions.

3.6 Case Study.

3.7 Accounting for Nuisance Effects.

3.8 Summary and Further Reading.

4 Bayesian Multiple Testing and False Discovery RateAnalysis.

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 BayesianClustering.

7.1 Introduction to Bayesian Clustering for Gene ExpressionData.

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 PredictiveInferences.

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.

"The target audience for this book is clearly
statisticians rather than biologists ... It does provide a very
useful overview of statistical genomics for anyone working in the
field." (The Quarterly Review of Biology, 1
March 2012)

"Bioinformatics researchers from many fields will find much
value in this book." (Mathematical Reviews, 2011)

"Experienced readers will find the review of advanced methods
for bioinformatics challenging and attainable. This book will
interest graduate students in statistics and bioinformatics
researchers from many fields." (Book News, December
2009)