Bayesian Analysis of Gene Expression Data

by Mallick, Bani K.; Gold, David; Baladandayuthapani, Veera

• ISBN13: 9780470517666
• ISBN10: 0470517662
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-08-24
• Publisher: Wiley

Summary

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.

Author Biography

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 Contents

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.