Genomics Data Analysis : False Discovery Rates and Empirical Bayes Methods book cover
1st Edition

Genomics Data Analysis
False Discovery Rates and Empirical Bayes Methods

ISBN 9780367280369
Published September 18, 2019 by Chapman and Hall/CRC
140 Pages 10 B/W Illustrations

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Book Description

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


Table of Contents

1. Basic probability and statistics

Biological background

Probability distributions

Probability functions

Contingency tables

Hypothesis tests and p values

Bibliographical notes

Exercises (PS1-PS3)

2. Introduction to likelihood

Likelihood function defined

Odds and probability: What’s the difference?

Bayesian uses of likelihood

Bibliographical notes 

Exercises (L1-L3)

3. False discovery rates


Local false discovery rate

Global and local false discovery rates

Computing the LFDR estimate

Bibliographical notes

Exercises (L4; A-B)

4. Simulating and analyzing gene expression data

Simulating gene expression with dice

DE games

Effects and Estimates (E&E)

Under the hood: normal distributions

Bibliographical notes

Exercises (C-E; G1-G4)

5. Variations in dimension and data


High-dimensional genetics

Subclasses and superclasses

Medium number of features

Bibliographical notes

Exercise (G5)

6. Correcting bias in estimates of the false discovery rate

Why correct the bias in estimates of the false discovery rate?

A misleading estimator of the false discovery rate 66

Corrected and re-ranked estimators of the local false discovery rate

Application to gene expression data analysis

Bibliographical notes

Exercises (CFDR0-CFDR3)

7. The L value: An estimated local false discovery rate to replace a p value

What if I only have one p value? Am I doomed?

The L value to the rescue!

The multiple-test L value

Bibliographical notes

Exercises (LV1-LV9)

8. Maximum likelihood and applications

Non-Bayesian uses of likelihood

Empirical Bayes uses of likelihood

Bibliographical notes

Exercises (M1-M2)

Appendix A. Generalized Bonferroni correction derived from conditional compatibility

A non-Bayesian approach to testing single and multiple hypotheses

Bibliographical notes

Appendix B. How to choose a method of hypothesis testing

Guidelines for scientists performing statistical hypothesis tests

Bibliographical notes

Appendix. Bibliography

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David R. Bickel is an Associate Professor in the Department of Biochemistry, Microbiology and Immunology of the University of Ottawa and a Core Member of the Ottawa Institute of Systems Biology. Since 2011, he has been teaching classes focused on the statistical analysis of genomics data. While working as a biostatistician in academia and industry, he has published new statistical methods for analyzing genomics data in leading statistics and bioinformatics journals. He is also investigating the foundations of statistical inference. For recent activity, see or follow him at @DavidRBickel (Twitter).