Probability and Statistics for Computer Science

ISBN-13: 9780470383421 / Angielski / Miękka / 2008 / 760 str.

James L. Johnson; Jr. Rex Johnson

Opis

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

Recenzje

"Undoubtedly, this is an excellent and well–organized book." ( Computing Reviews, August 27, 2008)

Spis treści

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.

O autorze

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.

Blurb

A unique probability guide for computer science

While many computer science curricula include only an introductory course on general probability, there is a recognized need for further study of this mathematical discipline within the specific context of computer science. Probability and Statistics for Computer Science develops introductory topics in probability with this particular emphasis, providing computer science students with an invaluable resource in their continued studies and professional research.

James Johnson′s text begins with the basic definitions of probability distributions and random variables and then elaborates their properties and applications. Probability and Statistics for Computer Science treats the most common discrete and continuous distributions, showing how they find use in decision and estimation problems, and constructs computer algorithms for generating observations from the various distributions. This one–of–a–kind resource also:

• Includes a thorough and rigorous development of all the necessary supporting mathematics

• Provides an opportunity to reconnect applications with the theoretical concepts of distributions introduced in prerequisite courses

• Gathers supporting topics in an appendix: set theory, limit processes, real number structure, Riemann–Stieltjes integrals, matrix transformation, and determinants

• Uses computer science examples such as client–server performance evaluation and image processing

The author also addresses a variety of supporting topics, such as estimation arguments with limits, properties of power series, and Markov processes. Johnson′s text proves an ideal resource for computer science students and practitioners interested in a probability study specific to their field.