Statistical Bioinformatics with R英文版
介绍
CHAPTER 1 Introduction ........................................................... 1
1.1 Statistical Bioinformatics....................................... 1
1.2 Genetics ............................................................. 3
1.3 Chi-Square Test ................................................... 6
1.4 The Cell and Its Function ...................................... 9
1.5 DNA ................................................................... 12
1.6 DNA Replication and Rearrangements .................... 14
1.7 Transcription and Translation................................ 15
1.8 Genetic Code....................................................... 16
1.9 Protein Synthesis ................................................. 19
Exercise 1 ........................................................... 20
Answer Choices for Questions 1 through 15 ............ 21
CHAPTER 2 Microarrays.............................................................. 23
2.1 Microarray Technology ......................................... 23
2.2 Issues in Microarray ............................................. 25
2.3 Microarray and Gene Expression and Its Uses ......... 29
2.4 Proteomics .......................................................... 30
Exercise 2 ........................................................... 31
CHAPTER 3 Probability and Statistical Theory ............................ 33
3.1 Theory of Probability ............................................ 34
3.2 Mathematical or Classical Probability ..................... 36
3.3 Sets .................................................................... 38
3.3.1 Operations on Sets ..................................... 39
3.3.2 Properties of Sets ....................................... 40
3.4 Combinatorics ..................................................... 41
3.5 Laws of Probability............................................... 44 v
vi Contents
3.6 Random Variables ................................................ 53
3.6.1 Discrete Random Variable ........................... 55
3.6.2 Continuous Random Variable ...................... 56
3.7 Measures of Characteristics of a Continuous
Probability Distribution ......................................... 57
3.8 Mathematical Expectation..................................... 57
3.8.1 Properties of Mathematical Expectation ........ 60
3.9 Bivariate Random Variable .................................... 62
3.9.1 Joint Distribution ....................................... 62
3.10 Regression .......................................................... 71
3.10.1 Linear Regression ...................................... 72
3.10.2 The Method of Least Squares ...................... 73
3.11 Correlation .......................................................... 78
3.12 Law of Large Numbers and Central
Limit Theorem ..................................................... 80
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
4.5.1 Properties of Poisson Distribution................. 88
4.6 Negative Binomial Distribution .............................. 89
4.7 Geometric Distribution.......................................... 92
4.7.1 Lack of Memory ......................................... 93
4.8 Hypergeometric Distribution ................................. 94
4.9 Multinomial Distribution ....................................... 95
4.10 Rectangular (or Uniform) Distribution ..................... 99
4.11 Normal Distribution .............................................. 100
4.11.1 Some Important Properties of Normal
Distribution and Normal Probability Curve .... 101
4.11.2 Normal Approximation to the Binomial ......... 106
4.12 Gamma Distribution ............................................. 107
4.12.1 Additive Property of Gamma Distribution ...... 108
4.12.2 Limiting Distribution of Gamma
Distribution ............................................... 108
4.12.3 Waiting Time Model ................................... 108
Contents vii
4.13 The Exponential Distribution ................................. 109
4.13.1 Waiting Time Model ................................... 110
4.14 Beta Distribution .................................................. 110
4.14.1 Some Results ............................................. 111
4.15 Chi-Square Distribution......................................... 111
4.15.1 Additive Property of Chi-Square
Distribution ............................................... 112
4.15.2 Limiting Distribution of Chi-Square
Distribution ............................................... 112
CHAPTER 5 Statistical Inference and Applications...................... 113
5.1 Introduction ........................................................ 113
5.2 Estimation........................................................... 115
5.2.1 Consistency............................................... 115
5.2.2 Unbiasedness ............................................ 116
5.2.3 Efficiency .................................................. 118
5.2.4 Sufficiency................................................. 120
5.3 Methods of Estimation .......................................... 121
5.4 Confidence Intervals............................................. 122
5.5 Sample Size ......................................................... 132
5.6 Testing of Hypotheses .......................................... 133
5.6.1 Tests about a Population Mean .................... 138
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
6.5.1 Wilcoxon Rank Sum Test ............................. 169
6.5.2 Mann-Whitney Test.................................... 171
6.6 The Scale Problem................................................ 174
6.6.1 Ansari-Bardley Test.................................... 175
6.6.2 Lepage Test .............................................. 178
6.6.3 Kolmogorov-Smirnov Test............................ 180
viii Contents
6.7 Gene Selection and Clustering of Time-Course or
Dose-Response Gene Expression Profiles ................ 182
6.7.1 Single Fractal Analysis................................ 184
6.7.2 Order-Restricted Inference .......................... 186
CHAPTER 7 Bayesian Statistics ................................................... 189
7.1 Bayesian Procedures ............................................ 189
7.2 Empirical Bayes Methods ...................................... 192
7.3 Gibbs Sampler ..................................................... 193
CHAPTER 8 Markov Chain Monte Carlo ...................................... 203
8.1 The Markov Chain................................................ 204
8.2 Aperiodicity and Irreducibility ............................... 213
8.3 Reversible Markov Chains..................................... 218
8.4 MCMC Methods in Bioinformatics .......................... 220
CHAPTER 9 Analysis of Variance ................................................ 227
9.1 One-Way ANOVA ................................................ 228
9.2 Two-Way Classification of ANOVA......................... 241
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
10.6.1 2n-Factorial Experiment .............................. 279
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
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发表于 2013-2-15 11:59:28