Introduction to Statistical Pattern Recognition

Contents......Page 5
Preface to the Sixth Edition......Page 11
Preface to the Fifth Edition......Page 13
1.2. Sample Space and Events......Page 17
1.3. Probabilities Defined on Events......Page 20
1.4. Conditional Probabilities......Page 23
1.5. Independent Events......Page 26
1.6. Bayes' Formula......Page 28
Exercises 1......Page 31
References......Page 36
2.1. Random Variables......Page 37
2.2. Discrete Random Variables......Page 41
2.2.2. The Binomial Random Variable......Page 42
2.2.3. The Geometric Random Variable......Page 45
2.2.4. The Poisson Random Variable......Page 46
2.3. Continuous Random Variables......Page 47
2.3.1. The Uniform Random Variable......Page 48
2.3.4. Normal Random Variables......Page 50
2.4.1. The Discrete Case......Page 52
2.4.2. The Continuous Case......Page 55
2.4.3. Expectation of a Function of a Random Variable......Page 56
2.5.1. Joint Distribution Functions......Page 60
2.5.2. Independent Random Variables......Page 64
2.5.3. Covariance and Variance of Sums of Random Variables......Page 65
2.5.4. Joint Probability Distribution of Functions of Random Variables......Page 74
2.6. Moment Generating Functions......Page 76
2.6.1. The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population......Page 84
2.7. Limit Theorems......Page 87
2.8. Stochastic Processes......Page 93
Exercises 2......Page 95
References......Page 106
3.2. The Discrete Case......Page 107
3.3. The Continuous Case......Page 112
3.4. Computing Expectations by Conditioning......Page 115
3.5. Computing Probabilities by Conditioning......Page 127
3.6.1. A List Model......Page 140
3.6.2. A Random Graph......Page 142
3.6.3. Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics......Page 149
3.6.4. The k-Record Values of Discrete Random Variables......Page 153
Exercises 3......Page 157
4.1. Introduction......Page 175
4.2. Chapman-Kolmogorov Equations......Page 178
4.3. Classification of States......Page 181
4.4. Limiting Probabilities......Page 190
4.5.1. The Gambler's Ruin Problem......Page 201
4.5.2. A Model for Algorithmic Efficiency......Page 204
4.5.3. Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem......Page 207
4.6. Mean Time Spent in Transient States......Page 213
4.7. Branching Processes......Page 215
4.8. Time Reversible Markov Chains......Page 219
4.9. Markov Chain Monte Carlo Methods......Page 229
4.10. Markov Decision Processes......Page 235
Exercises 4......Page 239
References......Page 252
5.1. Introduction......Page 253
5.2.1. Definition......Page 254
5.2.2. Properties of the Exponential Distribution......Page 255
5.2.3. Further Properties of the Exponential Distribution......Page 260
5.2.4. Convolutions of Exponential Random Variables......Page 263
5.3.1. Counting Processes......Page 267
5.3.2. Definition of the Poisson Process......Page 268
5.3.3. Interarrival and Waiting Time Distributions......Page 273
5.3.4. Further Properties of Poisson Processes......Page 275
5.3.5. Conditional Distribution of the Arrival Times......Page 281
5.3.6. Estimating Software Reliability......Page 293
5.4.1. Nonhomogeneous Poisson Process......Page 295