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E-raamat: Genomics Data Analysis: False Discovery Rates and Empirical Bayes Methods [Taylor & Francis e-raamat]

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  • Formaat: 140 pages, 10 Illustrations, black and white
  • Ilmumisaeg: 18-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9780429299308
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Genomics Data Analysis: False Discovery Rates and Empirical Bayes MethodsSuurem pilt
  • Formaat: 140 pages, 10 Illustrations, black and white
  • Ilmumisaeg: 18-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9780429299308
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429299308
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
Preface xi
Chapter 1 Basic Probability and Statistics
1(12)
1.1 Biological Background
1(2)
1.1.1 Genomics Terminology
1(1)
1.1.2 Microarray Gene Expression
2(1)
1.2 Probability Distributions
3(3)
1.3 Probability Functions
6(2)
1.4 Contingency Tables
8(3)
1.5 Hypothesis Tests And P Values
11(1)
1.6 Bibliographical Notes
12(1)
1.7 Exercises (PS1-PS3)
12(1)
Chapter 2 Introduction to Likelihood 13
2.1 Likelihood Function Defined
13(2)
2.2 Odds And Probability: What's The Difference?
15(1)
2.3 Bayesian Uses of Likelihood
16(3)
2.3.1 Bayesian Updating
16(1)
2.3.2 Bounds from p Values
17(2)
2.4 Bibliographical Notes
19(1)
2.5 Exercises (L1-L3)
20(1)
Chapter 3 False Discovery Rates
21(14)
3.1 Introduction
21(1)
3.2 Local False Discovery Rate
22(3)
3.2.1 Local False Discovery Rate Defined
22(2)
3.2.2 The LFDR, Posterior Odds, and Likelihood
24(1)
3.3 Nonlocal And Local False Discovery Rates
25(6)
3.4 Computing the Lfdr Estimate
31(1)
3.5 Bibliographical Notes
31(1)
3.6 Exercises (L4; A-B)
32(3)
Chapter 4 Simulating and Analyzing Gene Expression Data
35(22)
4.1 Simulating Gene Expression With Dice
36(2)
4.2 De Games
38(4)
4.2.1 Basic DE
39(1)
4.2.2 Advanced DE
40(2)
4.3 Effects and Estimates (E&E)
42(4)
4.3.1 Contrast with the DE Games
42(1)
4.3.2 Generating Mean Expression Levels
42(2)
4.3.3 Estimation of Effect Sizes
44(1)
4.3.4 Scoring
45(1)
4.4 Under the Hood: Normal Distributions
46(3)
4.4.1 Advanced DE's Normal Distributions
46(1)
4.4.2 E&E's Normal Distributions
47(2)
4.5 Bibliographical Notes
49(1)
4.6 Exercises (C--E; G1--G4)
49(8)
Chapter 5 Variations in Dimension and Data
57(16)
5.1 Introduction
57(1)
5.2 High-Dimensional Genetics
58(2)
5.3 Subclasses and Superclasses
60(3)
5.4 Medium Number of Features
63(7)
5.4.1 Empirical Bayes Methods
63(2)
5.4.2 Applications to Data of Medium Dimension
65(5)
5.5 Bibliographical Notes
70(1)
5.6 Exercise (G5)
71(2)
Chapter 6 Correcting Bias in Estimates of the False Discovery Rate
73(8)
Background
73(1)
6.1 Why Correct the Bias in Estimates of the False Discovery Rate?
74(1)
6.2 A Misleading Estimator of the False Discovery Rate
75(2)
6.3 Corrected and Re-Ranked Estimators of the Local False Discovery Rate
77(1)
6.4 Application to Gene Expression Data Analysis
78(1)
6.5 Bibliographical Notes
78(1)
6.6 Exercises (CFDR0-CFDR3)
79(2)
Chapter 7 The L Value: An Estimated Local False Discovery Rate to Replace a p Value
81(8)
7.1 What If I Only Have One p Value? Am I Doomed?
82(1)
7.2 The L Value to the Rescue!
83(1)
7.3 The Multiple-Test X Value
84(1)
7.4 Bibliographical Notes
85(1)
7.5 Exercises (LV1-LV9)
86(3)
Chapter 8 Maximum Likelihood and Applications
89(12)
8.1 Non-Bayesian Uses of Likelihood
89(5)
8.1.1 Maximum Likelihood Estimation
89(1)
8.1.2 Likelihood-Based p Values
90(1)
8.1.3 Likelihood-Based Confidence Intervals
91(3)
8.2 Empirical Bayes Uses of Likelihood
94(3)
8.2.1 Error Model for -omics Data
94(1)
8.2.2 Likelihood for -omics Data
95(2)
8.2.3 MLE for -omics Data
97(1)
8.3 Bibliographical Notes
97(1)
8.4 Exercises (M1-M2)
98(3)
Appendix A Generalized Bonferroni Correction Derived from Conditional Compatibility 101(6)
Appendix B How to Choose a Method of Hypothesis Testing 107(4)
Bibliography 111(6)
Index 117
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 davidbickel.com or follow him at @DavidRBickel (Twitter).
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