Bayesian Analysis of Gene Expression Data

This book provides an introduction to both Bayesian methods and gene expression, accessible to people with backgrounds in either. The text is enhanced by the inclusion of numerous problems and solutions, designed with an emphasis on methodology and application. There is also a supplementary website including the relevant software and further datasets. The book provides an extensive review of Bayesian analysis and advanced topics for bioinformatics, including an advanced section that extensively details the necessary applications and offers an introduction to the computational methods required for Bayesian statistics.The book is split into four parts, Part I introducing the fundamentals of Bayesian statistics, both modeling and computation. Part II builds on this, providing a more detailed introduction to the computational methods necessary for Bayesian statistics. Part III presents an introduction to the basic biology needed to work with microarrays, written specifically to enable those readers with no experience in the laboratory to understand. Part IV elaborates extensively on applications, including advanced topics for Bioinformatics research.

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
Bioinformatics and Gene Expression Experiments
Introduction
About This Book
Basic Biology
Background
DNA Structures and Transcription
Gene Expression Microarray Experiments
Bayesian Linear Models for Gene Expression
Introduction
Bayesian Analysis of a Linear Model
Bayesian Linear Models for Differential Expression
Bayesian ANOVA for Gene Selection
Robust ANOVA model with Mixtures of Singular Distributions
Case Study
Accounting for Nuisance Effects
Summary and Further Reading
Bayesian Multiple Testing and False Discovery Rate Analysis
Introduction to Multiple Testing
False Discovery Rate Analysis
Bayesian False Discovery Rate Analysis
Bayesian Estimation of FDR
FDR and Decision Theory
FDR and bFDR Summary
Bayesian Classification for Microarray Data
Introduction
Classification and Discriminant Rules
Bayesian Discriminant Analysis
Bayesian Regression Based Approaches to Classification
Bayesian Nonlinear Classification
Prediction and Model Choice
Examples
Discussion
Bayesian Hypothesis Inference for Gene Classes
Interpreting Microarray Results
Gene Classes
Bayesian Enrichment Analysis
Multivariate Gene Class Detection
Summary
Unsupervised Classification and Bayesian Clustering
Introduction to Bayesian Clustering for Gene Expression Data
Hierarchical Clustering
K-Means Clustering
Model-Based Clustering
Model-Based Agglomerative Hierarchical Clustering
Bayesian Clustering
Principal Components
Mixture Modeling
Label Switching
Clustering Using Dirichlet Process Prior
Infinite Mixture of Gaussian Distributions
Bayesian Graphical Models
Introduction
Probabilistic Graphical Models
Bayesian Networks
Inference for Network Models
Advanced Topics
Introduction
Analysis of Time Course Gene Expression Data
Survival Prediction Using Gene Expression Data
Basics of Bayesian Modeling
Basics
The General Representation Theorem
Bayes' Theorem
Models Based on Partial Exchangeability
Modeling with Predictors
Prior Distributions
Decision Theory and Posterior and Predictive Inferences
Predictive Distributions
Examples
Bayesian Model Choice
Hierarchical Modeling
Bayesian Mixture Modeling
Bayesian Model Averaging
Bayesian Computation Tools
Overview
Large-Sample Posterior Approximations
The Bayesian Central Limit Theorem
Laplace's Method
Monte Carlo Integration
Importance Sampling
Rejection Sampling
Gibbs Sampling
The Metropolis Algorithm and Metropolis-Hastings
Advanced Computational Methods
Block MCMC
Truncated Posterior Spaces
Latent Variables and the Auto-Probit Model
Bayesian Simultaneous Credible Envelopes
Proposal Updating
Posterior Convergence Diagnostics
MCMC Convergence and the Proposal
Graphical Checks for MCMC Methods
Convergence Statistics
MCMC in High-Throughput Analysis
Summary
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Bayesian Analysis of Gene Expression Data

Summary

Author Biography

Table of Contents

Supplemental Materials