The Probability Companion For Engineering And Computer Science

Description

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overview for students. Cover......Page 1 Front Matter ......Page 3 The Probability Companion for Engineering and Computer Science......Page 5 Copyright ......Page 6 Contents ......Page 7 Preface ......Page 13 Nomenclature......Page 15 1 Introduction......Page 19 2 Survey of Distributions......Page 43 3 Monte Carlo......Page 63 4 Discrete Random Variables......Page 77 5 The Normal Distribution......Page 92 6 Handling Experimental Data......Page 128 7 Mathematics of Random Variables......Page 150 8 Bayes......Page 205 9 Entropy......Page 276 10 Collective Behaviour......Page 311 11 Markov Chains......Page 326 12 Stochastic Processes......Page 367 Appendix A. Answers to Exercises......Page 409 Appendix B. Probability Distributions......Page 463 Bibliography ......Page 467 Index......Page 472