Statistical bioinformatics with R

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 5
PREFACE......Page 10
ACKNOWLEDGMENTS......Page 16
Contents......Page 9
1.1 Statistical Bioinformatics......Page 18
1.2 Genetics......Page 20
1.3 Chi-Square Test......Page 23
1.4 The Cell and Its Function......Page 26
1.5 DNA......Page 29
1.6 DNA Replication and Rearrangements......Page 31
1.7 Transcription and Translation......Page 32
1.8 Genetic Code......Page 33
1.9 Protein Synthesis......Page 36
Exercise 1......Page 37
Answer Choices for Questions 1 through 15......Page 38
2.1 Microarray Technology......Page 40
2.2 Issues in Microarray......Page 42
2.3 Microarray and Gene Expression and Its Uses......Page 46
2.4 Proteomics......Page 47
Exercise 2......Page 48
CHAPTER 3 Probability and Statistical Theory......Page 50
3.1 Theory of Probability......Page 51
3.2 Mathematical or Classical Probability......Page 53
3.3 Sets......Page 55
3.3.1 Operations on Sets......Page 56
3.3.2 Properties of Sets......Page 57
3.4 Combinatorics......Page 58
3.5 Laws of Probability......Page 61
3.6 Random Variables......Page 70
3.6.1 Discrete Random Variable......Page 72
3.6.2 Continuous Random Variable......Page 73
3.8 Mathematical Expectation......Page 74
3.8.1 Properties of Mathematical Expectation......Page 77
3.9.1 Joint Distribution......Page 79
3.10 Regression......Page 88
3.10.1 Linear Regression......Page 89
3.10.2 The Method of Least Squares......Page 90
3.11 Correlation......Page 95
3.12 Law of Large Numbers and Central Limit Theorem......Page 97
4.1 Introduction......Page 100
4.4 Binomial Distribution......Page 101
4.5 Poisson Distribution......Page 104
4.5.1 Properties of Poisson Distribution......Page 105
4.6 Negative Binomial Distribution......Page 106
4.7 Geometric Distribution......Page 109
4.7.1 Lack of Memory......Page 110
4.8 Hypergeometric Distribution......Page 111
4.9 Multinomial Distribution......Page 112
4.10 Rectangular (or Uniform) Distribution......Page 116
4.11 Normal Distribution......Page 117
4.11.1 Some Important Properties of Normal Distribution and Normal Probability Curve......Page 118
4.11.2 Normal Approximation to the Binomial......Page 123
4.12 Gamma Distribution......Page 124
4.12.3 Waiting Time Model......Page 125
4.13 The Exponential Distribution......Page 126
4.14 Beta Distribution......Page 127
4.15 Chi-Square Distribution......Page 128
4.15.2 Limiting Distribution of Chi-Square Distribution......Page 129
5.1 Introduction......Page 130
5.2.1 Consistency......Page 132
5.2.2 Unbiasedness......Page 133
5.2.3 Efficiency......Page 135
5.2.4 Sufficiency......Page 137
5.3 Methods of Estimation......Page 138
5.4 Confidence Intervals......Page 139
5.5 Sample Size......Page 149
5.6 Testing of Hypotheses......Page 150
5.6.1 Tests about a Population Mean......Page 155
5.7 Optimal Test of Hypotheses......Page 167
5.8 Likelihood Ratio Test......Page 173
CHAPTER 6 Nonparametric Statistics......Page 176
6.1 Chi-Square Goodness-of-Fit Test......Page 177
6.2 Kolmogorov-Smirnov One-Sample Statistic......Page 180
6.3 Sign Test......Page 181
6.4 Wilcoxon Signed-Rank Test......Page 183
6.5.1 Wilcoxon Rank Sum Test......Page 186
6.5.2 Mann-Whitney Test......Page 188
6.6 The Scale Problem......Page 191
6.6.1 Ansari-Bardley Test......Page 192
6.6.2 Lepage Test......Page 195
6.6.3 Kolmogorov-Smirnov Test......Page 197
6.7 Gene Selection and Clustering of Time-Course or Dose-Response Gene Expression Profiles......Page 199
6.7.1 Single Fractal Analysis......Page 201
6.7.2 Order-Restricted Inference......Page 203
7.1 Bayesian Procedures......Page 206
7.2 Empirical Bayes Methods......Page 209
7.3 Gibbs Sampler......Page 210
CHAPTER 8 Markov Chain Monte Carlo......Page 220
8.1 The Markov Chain......Page 221
8.2 Aperiodicity and Irreducibility......Page 230
8.3 Reversible Markov Chains......Page 235
8.4 MCMC Methods in Bioinformatics......Page 237
CHAPTER 9 Analysis of Variance......Page 244
9.1 One-Way ANOVA......Page 245
9.2 Two-Way Classification of ANOVA......Page 258
10.1 Introduction......Page 270
10.2 Principles of the Design of Experiments......Page 272
10.3 Completely Randomized Design......Page 273
10.4 Randomized Block Design......Page 279
10.5 Latin Square Design......Page 287
10.6 Factorial Experiments......Page 295
10.6.1 2n-Factorial Experiment......Page 296
10.7 Reference Designs and Loop Designs......Page 303
11.1 Introduction......Page 310
11.2 Type I Error and FDR......Page 311
11.3 Multiple Testing Procedures......Page 314
REFERENCES\n......Page 322
INDEX......Page 332