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Probability Companion for Engineering and Computer Science [Kõva köide]

4.50/5 (2 hinnangut Goodreads-ist)
(University of Southampton)
  • Formaat: Hardback, 470 pages, kõrgus x laius x paksus: 260x183x26 mm, kaal: 1130 g, Worked examples or Exercises; 356 Line drawings, black and white
  • Ilmumisaeg: 23-Jan-2020
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108480535
  • ISBN-13: 9781108480536
Teised raamatud teemal:
Probability Companion for Engineering and Computer ScienceSuurem pilt
  • Formaat: Hardback, 470 pages, kõrgus x laius x paksus: 260x183x26 mm, kaal: 1130 g, Worked examples or Exercises; 356 Line drawings, black and white
  • Ilmumisaeg: 23-Jan-2020
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108480535
  • ISBN-13: 9781108480536
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108480536.html
Märksõnad:
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.

Arvustused

'In addition to the usual topics of probability theory, a large portion of the book is devoted to presenting modern applications including Bayesian inference and MCMC. Students will appreciate the detailed derivations of formulas and the full solutions of problems. The text is interspersed with personal viewpoints and advice, which gives the book the flavour of a lively lecture by an enthusiastic teacher.' Robert Piché, Tampereen yliopisto, Finland 'Adam Prügel-Bennett has created a great toolbox for all scientists working with models that take into account the uncertainty of the real world.' Wolfram Burgard, Albert-Ludwigs-Universität Freiburg, Germany 'This is a wonderful book, one that I wish I'd had when learning about probability. Indeed, there are lots of gems in there that I'm looking forward to reading about myself! The book is beautifully illustrated and refreshingly full of insight, without overly formal mathematical jargon. This book would appeal to students and researchers that are competent in mathematics and delight in gaining a deeper understanding of the subject, both from an intuitive and mathematical standpoint. It excels in demonstrating the wide applicability of probabilistic approaches to problem solving and modelling. This book deserves to be on the shelf of any researcher that uses probability to solve problems.' David Barber, University College London 'The book can be very recommended all readers, who are interested in this field.' Ludwig Paditz, Theatre and Performance Theory

Muu info

Using examples and building intuition, this friendly guide helps readers understand and use probabilistic tools from basic to sophisticated.
Preface xi
Nomenclature xiii
1 Introduction 1(24)
1.1 Why Probabilities?
2(1)
1.2 Events and Probabilities
3(8)
1.2.1 Events
3(2)
1.2.2 Assigning Probabilities
5(1)
1.2.3 Joint and Conditional Probabilities
5(3)
1.2.4 Independence
8(3)
1.3 Random Variables
11(1)
1.4 Probability Densities
12(3)
1.5 Expectations
15(4)
1.5.1 Indicator Functions
16(1)
1.5.2 Statistics
17(2)
1.6 Probabilistic Inference
19(4)
1.A Measure for Measure
23(2)
2 Survey of Distributions 25(20)
2.1 Discrete Distributions
26(4)
2.1.1 Binomial Distribution
26(1)
2.1.2 Hypergeometric Distribution
27(1)
2.1.3 Poisson Distribution
28(2)
2.2 Continuous Distributions
30(5)
2.2.1 Normal Distribution
30(1)
2.2.2 Gamma Distribution
31(3)
2.2.3 Beta Distribution
34(1)
2.2.4 Cauchy Distribution
35(1)
2.3 Multivariate Distributions
35(3)
2.3.1 Multinomial Distribution
35(2)
2.3.2 Multivariate Normal Distribution
37(1)
2.3.3 Dirichlet Distribution
37(1)
2.4 Exponential Family
38(3)
2.A The Gamma Function
41(2)
2.B The Beta Function
43(2)
3 Monte Carlo 45(14)
3.1 Random Deviates
46(3)
3.1.1 Estimating Expectations
46(1)
3.1.2 Monte Carlo Integration
47(2)
3.2 Uniform Random Deviates
49(2)
3.3 Non-Uniform Random Deviates
51(8)
3.3.1 Transformation Method
51(3)
3.3.2 Rejection Sampling
54(2)
3.3.3 Multivariate Deviates
56(3)
4 Discrete Random Variables 59(15)
4.1 Bernoulli Trials
60(1)
4.2 Binomial Distribution
61(5)
4.2.1 Statistical Properties of the Binomial Distribution
62(2)
4.2.2 Cumulants
64(2)
4.3 Beyond the Binomial Distribution
66(8)
4.3.1 Large n Limit
66(1)
4.3.2 Poisson Distribution
67(1)
4.3.3 Multinomial Distribution
68(6)
5 The Normal Distribution 74(36)
5.1 Ubiquitous Normals
75(1)
5.2 Basic Properties
76(5)
5.2.1 Integrating Gaussians
76(2)
5.2.2 Moments and Cumulants
78(3)
5.3 Central Limit Theorem
81(9)
5.4 Cumulative Distribution Function of a Normal Distribution
90(2)
5.5 Best of n
92(4)
5.6 Multivariate Normal Distributions
96(7)
5.A Dirac Delta
103(4)
5.B Characteristic Function for the Cauchy Distribution
107(3)
6 Handling Experimental Data 110(22)
6.1 Estimating the Error in the Mean
111(4)
6.1.1 Computing Means with Errors
114(1)
6.1.2 Bernoulli Trials
114(1)
6.2 Histogram
115(1)
6.3 Significance Tests
116(7)
6.4 Maximum Likelihood Estimate
123(3)
6.A Deriving the T-Distribution
126(6)
7 Mathematics of Random Variables 132(55)
7.1 Convergence
133(9)
7.1.1 Laws of Large Numbers
138(1)
7.1.2 Martingales
139(3)
7.2 Inequalities
142(24)
7.2.1 Cauchy-Schwarz Inequality
142(1)
7.2.2 Markov's Inequality
143(6)
7.2.3 Chebyshev's Inequality
149(3)
7.2.4 Tail Bounds and Concentration Theorems
152(5)
7.2.5 Chernoff Bounds for Independent Bernoulli Trials
157(2)
7.2.6 Jensen's Inequality
159(6)
7.2.7 Union Bound
165(1)
7.3 Comparing Distributions
166(11)
7.3.1 Kullback-Leibler Divergence
166(4)
7.3.2 Wasserstein Distance
170(7)
7.A Taylor Expansion
177(2)
7.B Hoeffding's Bound for Negatively Correlated Random Boolean Variables
179(3)
7.C Constrained Optimisation
182(5)
8 Bayes 187(71)
8.1 Bayesian Statistics
188(9)
8.2 Performing Bayesian Inference
197(17)
8.2.1 Conjugate Priors
198(7)
8.2.2 Uninformative Priors
205(6)
8.2.3 Model Selection
211(3)
8.3 Bayes with Complex Likelihoods
214(13)
8.3.1 Hierarchical Models
214(1)
8.3.2 MAP Solution
215(5)
8.3.3 Variational Approximation
220(7)
8.4 Latent Variable Models
227(16)
8.4.1 Hidden Markov Models
235(5)
8.4.2 Variational Auto-Encoders
240(3)
8.5 Machine Learning
243(13)
8.5.1 Naive Bayes Classifier
244(1)
8.5.2 Graphical Models
245(11)
8.A Bertrand's Paradox
256(2)
9 Entropy 258(35)
9.1 Shannon Entropy
259(8)
9.1.1 Information Theory
259(6)
9.1.2 Properties of Entropy
265(2)
9.2 Applications
267(9)
9.2.1 Mutual Information
267(1)
9.2.2 Maximum Entropy
267(5)
9.2.3 The Second Law of Thermodynamics
272(4)
9.3 Beyond Information Theory
276(14)
9.3.1 Kolmogorov Complexity
276(1)
9.3.2 Minimum Description Length
277(8)
9.3.3 Fisher Information
285(5)
9.A Functionals
290(3)
10 Collective Behaviour 293(15)
10.1 Random Walk
294(1)
10.2 Branching Processes
295(2)
10.3 Percolation
297(2)
10.4 Ising Model
299(3)
10.5 Self-Organised Criticality
302(2)
10.6 Disordered Systems
304(4)
11 Markov Chains 308(41)
11.1 Markov Chains
309(8)
11.1.1 Markov Chains and Stochastic Matrices
310(3)
11.1.2 Properties of Stochastic Matrices
313(3)
11.1.3 Ergodic Stochastic Matrices
316(1)
11.2 Markov Chain Monte Carlo
317(13)
11.2.1 Detailed Balance
318(5)
11.2.2 Bayes and MCMC
323(3)
11.2.3 Convergence of MCMC
326(3)
11.2.4 Hybrid Monte Carlo
329(1)
11.3 Kalman and Particle Filtering
330(17)
11.3.1 The Kalman Filter
332(6)
11.3.2 Particle Filtering
338(6)
11.3.3 Approximate Bayesian Computation
344(3)
11.A Eigenvalues and Eigenvectors of General Square Matrices
347(2)
12 Stochastic Processes 349(42)
12.1 Stochastic Processes
350(9)
12.1.1 What Are Stochastic Processes?
350(1)
12.1.2 Gaussian Processes
351(5)
12.1.3 Markov Processes
356(3)
12.2 Diffusion Processes
359(21)
12.2.1 Brownian Motion
359(2)
12.2.2 Stochastic Differential Equations
361(9)
12.2.3 Fokker-Planck Equation
370(4)
12.2.4 Stationary Distribution of Stochastic Processes
374(3)
12.2.5 Pricing Options
377(3)
12.3 Point Processes
380(11)
12.3.1 Poisson Processes
380(3)
12.3.2 Poisson Processes in One Dimension
383(2)
12.3.3 Chemical Reactions
385(6)
A Answers to Exercises 391(54)
A.1 Answers to
Chapter
1. Introduction
392(4)
A.2 Answers to
Chapter
2. Survey of Distributions
396(3)
A.3 Answers to
Chapter
3. Monte Carlo
399(2)
A.4 Answers to
Chapter
4. Discrete Random Variables
401(6)
A.5 Answers to
Chapter
5. The Normal Distribution
407(4)
A.6 Answers to
Chapter
6. Handling Experimental Data
411(3)
A.7 Answers to
Chapter
7. Mathematics of Random Variables
414(7)
A.8 Answers to
Chapter
8. Bayes
421(6)
A.9 Answers to
Chapter
9. Entropy
427(3)
A.10 Answers to
Chapter
10. Collective Behaviour
430(2)
A.11 Answers to
Chapter
11. Markov Chains
432(9)
A.12 Answers to
Chapter
12. Stochastic Processes
441(4)
B Probability Distributions 445(4)
Table B1 Discrete Univariate Distributions
446(1)
Table B2 Continuous Univariate Distributions
447(1)
Table B3 Continuous and Discrete Multivariate Distributions
448(1)
Bibliography 449
Index 45
Adam Prügel-Bennett is Professor of Electronics and Computer Science at the University of Southampton. He received his Ph.D. in Statistical Physics at the University of Edinburgh, where he became interested in disordered and complex systems. He currently researches in the area of mathematical modelling, optimisation and machine learning and has published many papers on these subjects.