Genomics Data Analysis

False Discovery Rates and Empirical Bayes Methods

David R. Bickel

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9781032475288
• eBook ISBN: 9781000707090
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Statisticians have met the need to test hundreds or thousands of genomics hypotheses simultaneously with novel empirical Bayes methods that combine advantages of traditional Bayesian and frequentist statistics. Techniques for estimating the local false discovery rate assign probabilities of differential gene expression, genetic association, etc. without requiring subjective prior distributions. This book brings these methods to scientists while keeping the mathematics at an elementary level. Readers will learn the fundamental concepts behind local false discovery rates, preparing them to analyze their own genomics data and to critically evaluate published genomics research.Key Features: * dice games and exercises, including one using interactive software, for teaching the concepts in the classroom* examples focusing on gene expression and on genetic association data and briefly covering metabolomics data and proteomics data* gradual introduction to the mathematical equations needed* how to choose between different methods of multiple hypothesis testing* how to convert the output of genomics hypothesis testing software to estimates of local false discovery rates* guidance through the minefield of current criticisms of p values* material on non-Bayesian prior p values and posterior p values not previously published

Chapter 1

Basic Probability and Statistics

This Godfrey Norton was evidently an important factor in the matter. He was a lawyer. That sounded ominous. What was the relation between them, and what the object of his repeated visits? Was she his client, his friend, or his mistress? If the former, she had probably transferred the photograph to his keeping. If the latter, it was less likely. On the issue of this question depended whether I should continue my work at Briony Lodge, or turn my attention to the gentleman’s chambers in the Temple. It was a delicate point, and it widened the field of my inquiry. I fear that I bore you with these details, but I have to let you see my little difficulties, if you are to understand the situation.

1.1 Biological background

1.1.1 Genomics Terminology

Since it is assumed that you have a knowledge of the basics of modern biology, it may be helpful to refresh your memory on (or to get up to speed with) terminology used in genomics. Knowing elementary biological concepts will help you learn the statistical concepts since the latter are explained in terms of biological examples.

1.1.2 Microarray Gene Expression

A gene is a unit of inherited biological information that influences various functions in an organism. A gene is said to be expressed if it is active in the sense of producing material that can potentially start, stop, or modify an organism’s chemical, physiological, or behavioral functions. Microarray technology enables the simultaneous measurement of the expression level of each of thousands of genes from a biological sample drawn from a tissue such as the bone tissue of an animal or the stem tissue of ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Chapter 1: Basic Probability and Statistics
• Chapter 2: Introduction to Likelihood
• Chapter 3: False Discovery Rates
• Chapter 4: Simulating and Analyzing Gene Expression Data
• Chapter 5: Variations in Dimension and Data
• Chapter 6: Correcting Bias in Estimates of the False Discovery Rate
• Chapter 7: The ℒ Value: An Estimated Local False Discovery Rate to Replace a p Value
• Chapter 8: Maximum Likelihood and Applications
• Appendix A: Generalized Bonferroni Correction Derived from Conditional Compatibility
• Appendix B: How to Choose a Method of Hypothesis Testing
• Bibliography
• Index