Statistical bioinformatics with R

Preface

Acknowledgments

Chapter 1. Introduction

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

3.3.1. Operations on Sets

3.3.2. Properties of Sets

3.4. Combinatorics

3.5. Laws of Probability

3.6. Random Variables

3.6.1. Discrete Random Variable

3.6.2. Continuous Random Variable

3.7. Measures of Characteristics of a Continuous Probability Distribution

3.8. Mathematical Expectation

3.8.1. Properties of Mathematical Expectation

3.9. Bivariate Random Variable

3.9.1. Joint Distribution

3.10. Regression

3.10.1. Linear Regression

3.10.2. The Method of Least Squares

3.11. Correlation

3.12. Law of Large Numbers and Central Limit Theorem

Chapter 4. Special Distributions, Properties, and Applications

4.1. Introduction

4.2. Discrete Probability Distributions

4.3. Bernoulli Distribution

4.4. Binomial Distribution

4.5. Poisson Distribution

4.5.1. Properties of Poisson Distribution

4.6. Negative Binomial Distribution

4.7. Geometric Distribution

4.7.1. Lack of Memory

4.8. Hypergeometric Distribution

4.9. Multinomial Distribution

4.10. Rectangular (or Uniform) Distribution

4.11. Normal Distribution

4.11.1. Some Important Properties of Normal Distribution and Normal Probability Curve

4.11.2. Normal Approximation to the Binomial

4.12. Gamma Distribution

4.12.1. Additive Property of Gamma Distribution

4.12.2. Limiting Distribution of Gamma Distribution

4.12.3. Waiting Time Model

4.13. The Exponential Distribution

4.13.1. Waiting Time Model

4.14. Beta Distribution

4.14.1. Some Results

4.15. Chi-Square Distribution

4.15.1. Additive Property of Chi-Square Distribution

4.15.2. Limiting Distribution of Chi-Square Distribution

Chapter 5. Statistical Inference and Applications

5.1. Introduction

5.2. Estimation

5.2.1. Consistency

5.2.2. Unbiasedness

5.2.3. Efficiency

5.2.4. Sufficiency

5.3. Methods of Estimation

5.4. Confidence Intervals

5.5. Sample Size

5.6. Testing of Hypotheses

5.6.1. Tests about a Population Mean

5.7. Optimal Test of Hypotheses

5.8. Likelihood Ratio Test

Chapter 6. Nonparametric Statistics

6.1. Chi-Square Goodness-of-Fit Test

6.2. Kolmogorov-Smirnov One-Sample Statistic

6.3. Sign Test

6.4. Wilcoxon Signed-Rank Test

6.5. Two-Sample Test

6.5.1. Wilcoxon Rank Sum Test

6.5.2. Mann-Whitney Test

6.6. The Scale Problem

6.6.1. Ansari-Bardley Test

6.6.2. Lepage Test

6.6.3. Kolmogorov-Smirnov Test

6.7. Gene Selection and Clustering of Time-Course or Dose-Response Gene Expression Profiles

6.7.1. Single Fractal Analysis

6.7.2. Order-Restricted Inference

Chapter 7. Bayesian Statistics

7.1. Bayesian Procedures

7.2. Empirical Bayes Methods

7.3. Gibbs Sampler

Chapter 8. Markov Chain Monte Carlo

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

9.1. One-Way ANOVA

9.2. Two-Way Classification of ANOVA

Chapter 10. The Design of Experiments

10.1. Introduction

10.2. Principles of the Design of Experiments

10.3. Completely Randomized Design

10.4. Randomized Block Design

10.5. Latin Square Design

10.6. Factorial Experiments

10.6.1. 2 n -Factorial Experiment

10.7. Reference Designs and Loop Designs

Chapter 11. Multiple Testing of Hypotheses

11.1. Introduction

11.2. Type I Error and FDR

11.3. Multiple Testing Procedures

References

Index