Statistical bioinformatics with R / Sunil K. Mathur. — Amsterdam : Academic, c2010. – (58.17115/M432) |
Contents
CONTENTS
PREFACE
ACKNOWLEDGMENTS
CHAPTER 1 Introduction 1
1.1 Statistical Bioinformatics
1.2 Genetics
1.3 Chi-Square Test
1.4 The Cell and Its Function
1.5 DNA
1.6 DNA Replication and Rearrangements
1.7 Transcription and Translation
1.8 Genetic Code
1.9 Protein Synthesis
Exercise 1
Answer Choices for Questions 1 through 15
CHAPTER 2 Microarrays
2.1 Microarray Technology
2.2 Issues in Microarray
2.3 Microarray and Gene Expression and Its Uses
2.4 Proteomics
Exercise 2
CHAPTER 3 Probability and Statistical Theory
3.1 Theory of Probability
3.2 Mathematical or Classical Probability
3.3 Sets
3.4 Combinatorics
3.5 Laws of Probability
3.6 Random Variables
3.7 Measures of Characteristics of a Continuous Probability Distribution
3.8 Mathematical Expectation
3.9 Bivariate Random Variable
3.10 Regression
3.11 Correlation
3.12 Law of Large Numbers and Central Limit Theorem
CHAPTER 4 Special Distributions, Properties, and Applications 83
4.1 Introduction 83
4.2 Discrete Probability Distributions 84
4.3 Bernoulli Distribution 84
4.4 Binomial Distribution 84
4.5 Poisson Distribution 87
4.6 Negative Binomial Distribution 89
4.7 Geometric Distribution 92
4.8 Hypergeometric Distribution 94
4.9 Multinomial Distribution 95
4.10 Rectangular (or Uniform) Distribution 99
4.11 Normal Distribution 100
4.12 Gamma Distribution 107
4.13 The Exponential Distribution 109
4.14 Beta Distribution 110
4.15 Chi-Square Distribution 111
CHAPTER 5 Statistical Inference and Applications 113
5.1 Introduction 113
5.2 Estimation 115
5.3 Methods of Estimation 121
5.4 Confidence Intervals 122
5.5 Sample Size 132
5.6 Testing of Hypotheses 133
5.7 Optimal Test of Hypotheses 150
5.8 Likelihood Ratio Test 156
CHAPTER 6 Nonparametric Statistics 159
6.1 Chi-Square Goodness-of-Fit Test 160
6.2 Kolmogorov Smirnov One-Sample Statistic 163
6.3 Sign Test 164
6.4 Wilcoxon Signed-Rank Test 166
6.5 Two-Sample Test 169
6.6 The Scale Problem 174
6.7 Gene Selection and Clustering of Time-Course or Dose-Response Gene Expression Profiles 182
CHAPTER 7 Bayesian Statistics 189
7.1 Bayesian Procedures
7.2 Empirical Bayes Methods
7.3 Gibbs Sampler
CHAPTER 8 Markov Chain Monte Carlo 203
8.1 The Markov Chain
8.2 Aperiodicity and Irreducibility
8.3 Reversible Markov Chains
8.4 MCMC Methods in Bioinformatics
CHAPTER 9 Analysis of Variance 227
9.1 One-Way ANOVA
9.2 Two-Way Classification of ANOVA
CHAPTER 10 The Design of Experiments 253
10.1 Introduction 253
10.2 Principles of the Design of Experiments 255
10.3 Completely Randomized Design 256
10.4 Randomized Block Design 262
10.5 Latin Square Design 270
10.6 Factorial Experiments 278
10.7 Reference Designs and Loop Designs 286
CHAPTER 11 Multiple Testing of Hypotheses 293
11.1 Introduction 293
11.2 Type I Error and FDR 294
11.3 Multiple Testing Procedures 297
REFERENCES 305
INDEX 315