Probability and Statistics for Computer Science
1. Auflage Januar 2008
760 Seiten, Softcover
Wiley & Sons Ltd
ISBN:
978-0-470-38342-1
John Wiley & Sons
Comprehensive and thorough development of both probability and
statistics for serious computer scientists; goal-oriented: "to
present the mathematical analysis underlying probability
results"
Special emphases on simulation and discrete decision theory
Mathematically-rich, but self-contained text, at a gentle
pace
Review of calculus and linear algebra in an appendix
Mathematical interludes (in each chapter) which examine
mathematical techniques in the context of probabilistic or
statistical importance
Numerous section exercises, summaries, historical notes, and
Further Readings for reinforcement of content
Preface.
1. Combinatorics and Probability.
1.1 Combinatorics.
1.2 Summations.
1.3 Probability spaces and random variables.
1.4 Conditional probability.
1.5 Joint distributions.
1.6 Summary.
2. Discrete Distributions.
2.1 The Bernoulli and binomial distributions.
2.2 Power series.
2.3 Geometric and negative binomial forms.
2.4 The Poisson distribution.
2.5 The hypergeometric distribution.
2.6 Summary.
3. Simulation.
3.1 Random number generation.
3.2 Inverse transforms and rejection filters.
3.3 Client-server systems.
3.4 Markov chains.
3.5 Summary.
4. Discrete Decision Theory.
4.1 Decision methods without samples.
4.2 Statistics and their properties.
4.3 Sufficient statistics.
4.4 Hypothesis testing.
4.5 Summary.
5. Real Line-Probability.
5.1 One-dimensional real distributions.
5.2 Joint random variables.
5.3 Differentiable distributions.
5.4 Summary.
6. Continuous Distributions.
6.1 The normal distributions.
6.2 Limit theorems.
6.3 Gamma and beta distributions.
6.4 The X² and related distributions.
6.5 Computer simulations.
6.6 Summary.
7. Parameter Estimation.
7.1 Bias, consistency, and efficiency.
7.2 Normal inference.
7.3 Sums of squares.
7.4 Analysis of variance.
7.5 Linear regression.
7.6 Summary.
A. Analytical Tools.
B. Statistical Tables.
Bibliography.
Index.
1. Combinatorics and Probability.
1.1 Combinatorics.
1.2 Summations.
1.3 Probability spaces and random variables.
1.4 Conditional probability.
1.5 Joint distributions.
1.6 Summary.
2. Discrete Distributions.
2.1 The Bernoulli and binomial distributions.
2.2 Power series.
2.3 Geometric and negative binomial forms.
2.4 The Poisson distribution.
2.5 The hypergeometric distribution.
2.6 Summary.
3. Simulation.
3.1 Random number generation.
3.2 Inverse transforms and rejection filters.
3.3 Client-server systems.
3.4 Markov chains.
3.5 Summary.
4. Discrete Decision Theory.
4.1 Decision methods without samples.
4.2 Statistics and their properties.
4.3 Sufficient statistics.
4.4 Hypothesis testing.
4.5 Summary.
5. Real Line-Probability.
5.1 One-dimensional real distributions.
5.2 Joint random variables.
5.3 Differentiable distributions.
5.4 Summary.
6. Continuous Distributions.
6.1 The normal distributions.
6.2 Limit theorems.
6.3 Gamma and beta distributions.
6.4 The X² and related distributions.
6.5 Computer simulations.
6.6 Summary.
7. Parameter Estimation.
7.1 Bias, consistency, and efficiency.
7.2 Normal inference.
7.3 Sums of squares.
7.4 Analysis of variance.
7.5 Linear regression.
7.6 Summary.
A. Analytical Tools.
B. Statistical Tables.
Bibliography.
Index.
"Undoubtedly, this is an excellent and well-organized book." (Computing Reviews, August 27, 2008)
James L. Johnson holds a PhD in mathematics from the University of Minnesota and has twenty-five years' experience in academic and industrial computer science. He is currently Professor of Computer Science at Western Washington University. He is also the author of Database: Models, Languages, Design.
