Bayesian Analysis of Gene Expression Data

by Bani K. Mallick (Texas A&M University, USA); David Gold (The State University Of New York, USA); Veera Baladandayuthapani (Texas A&M University, USA)

• ISBN13: 9780470742815
• ISBN10: 047074281X
• Format: eBook
• Copyright: 2009-07-01
• Publisher: Wiley

Summary

The field of high-throughput genetic experimentation is evolving rapidly, with the advent of new technologies and new venues for data mining. Bayesian methods play a role central to the future of data and knowledge integration in the field of Bioinformatics. This book is devoted exclusively to Bayesian methods of analysis for applications to high-throughput gene expression data, exploring the relevant methods that are changing Bioinformatics. Case studies, illustrating Bayesian analyses of public gene expression data, provide the backdrop for students to develop analytical skills, while the more experienced readers will find the review of advanced methods challenging and attainable.This book:Introduces the fundamentals in Bayesian methods of analysis for applications to high-throughput gene expression data. Provides an extensive review of Bayesian analysis and advanced topics for Bioinformatics, including examples that extensively detail the necessary applications. Accompanied by website featuring datasets, exercises and solutions.Bayesian Analysis of Gene Expression Data offers a unique introduction to both Bayesian analysis and gene expression, aimed at graduate students in Statistics, Biomedical Engineers, Computer Scientists, Biostatisticians, Statistical Geneticists, Computational Biologists, applied Mathematicians and Medical consultants working in genomics. Bioinformatics researchers from many fields will find much value in this book.

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

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