Preface p. ix
Acknowledgments p. xv
Introduction p. 1
Statistical Bioinformatics p. 1
Genetics p. 3
Chi-Square Test p. 6
The Cell and Its Function p. 9
DNA p. 12
DNA Replication and Rearrangements p. 14
Transcription and Translation p. 15
Genetic Code p. 16
Protein Synthesis p. 19
Exercise 1 p. 20
Answer Choices for Questions 1 through 15 p. 21
Microarrays p. 23
Microarray Technology p. 23
Issues in Microarray p. 25
Microarray and Gene Expression and Its Uses p. 29
Proteomics p. 30
Exercise 2 p. 31
Probability and Statistical Theory p. 33
Theory of Probability p. 34
Mathematical or Classical Probability p. 36
Sets p. 38
Operations on Sets p. 39
Properties of Sets p. 40
Combinatorics p. 41
Laws of Probability p. 44
Random Variables p. 53
Discrete Random Variable p. 55
Continuous Random Variable p. 56
Measures of Characteristics of a Continuous Probability Distribution p. 57
Mathematical Expectation p. 57
Properties of Mathematical Expectation p. 60
Bivariate Random Variable p. 62
Joint Distribution p. 62
Regression p. 71
Linear Regression p. 72
The Method of Least Squares p. 73
Correlation p. 78
Law of Large Numbers and Central Limit Theorem p. 80
Special Distributions, Properties, and Applications p. 83
Introduction p. 83
Discrete Probability Distributions p. 84
Bernoulli Distribution p. 84
Binomial Distribution p. 84
Poisson Distribution p. 87
Properties of Poisson Distribution p. 88
Negative Binomial Distribution p. 89
Geometric Distribution p. 92
Lack of Memory p. 93
Hypergeometric Distribution p. 94
Multinomial Distribution p. 95
Rectangular (or Uniform) Distribution p. 99
Normal Distribution p. 100
Some Important Properties of Normal Distribution and Normal Probability Curve p. 101
Normal Approximation to the Binomial p. 106
Gamma Distribution p. 107
Additive Property of Gamma Distribution p. 108
Limiting Distribution of Gamma Distribution p. 108
Waiting Time Model p. 108
The Exponential Distribution p. 109
Waiting Time Model p. 110
Beta Distribution p. 110
Some Results p. 111
Chi-Square Distribution p. 111
Additive Property of Chi-Square Distribution p. 112
Limiting Distribution of Chi-Square Distribution p. 112
Statistical Inference and Applications p. 113
Introduction p. 113
Estimation p. 115
Consistency p. 115
Unbiasedness p. 116
Efficiency p. 118
Sufficiency p. 120
Methods of Estimation p. 121
Confidence Intervals p. 122
Sample Size p. 132
Testing of Hypotheses p. 133
Tests about a Population Mean p. 138
Optimal Test of Hypotheses p. 150
Likelihood Ratio Test p. 156
Nonparametric Statistics p. 159
Chi-Square Goodness-of-Fit Test p. 160
Kolmogorov-Smirnov One-Sample Statistic p. 163
Sign Test p. 164
Wilcoxon Signed-Rank Test p. 166
Two-Sample Test p. 169
Wilcoxon Rank Sum Test p. 169
Mann-Whitney Test p. 171
The Scale Problem p. 174
Ansari-Bardley Test p. 175
Lepage Test p. 178
Kolmogorov-Smirnov Test p. 180
Gene Selection and Clustering of Time-Course or Dose-Response Gene Expression Profiles p. 182
Single Fractal Analysis p. 184
Order-Restricted Inference p. 186
Bayesian Statistics p. 189
Bayesian Procedures p. 189
Empirical Bayes Methods p. 192
Gibbs Sampler p. 193
Markov Chain Monte Carlo p. 203
The Markov Chain p. 204
Aperiodicity and Irreducibility p. 213
Reversible Markov Chains p. 218
MCMC Methods in Bioinformatics p. 220
Analysis of Variance p. 227
One-Way ANOVA p. 228
Two-Way Classification of ANOVA p. 241
The Design of Experiments p. 253
Introduction p. 253
Principles of the Design of Experiments p. 255
Completely Randomized Design p. 256
Randomized Block Design p. 262
Latin Square Design p. 270
Factorial Experiments p. 278
2n-Factorial Experiment p. 279
Reference Designs and Loop Designs p. 286
Multiple Testing of Hypotheses p. 293
Introduction p. 293
Type I Error and FDR p. 294
Multiple Testing Procedures p. 297
References p. 305
Index p. 315
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