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Author: Bruce Hajek
Publisher: Cambridge University Press
ISBN: 1316241246
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author: Bruce Hajek
Publisher: Cambridge University Press
ISBN: 1316241246
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author: Dirk P. Kroese
Publisher: John Wiley & Sons
ISBN: 1118014952
Category : Mathematics
Languages : en
Pages : 627
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Book Description
A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Author: Scott Miller
Publisher: Academic Press
ISBN: 0123869811
Category : Mathematics
Languages : en
Pages : 625
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Book Description
Miller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. * Exceptional exposition and numerous worked out problems make the book extremely readable and accessible * The authors connect the applications discussed in class to the textbook * The new edition contains more real world signal processing and communications applications * Includes an entire chapter devoted to simulation techniques.
Author: Venkatarama Krishnan
Publisher: John Wiley & Sons
ISBN: 0471998281
Category : Mathematics
Languages : en
Pages : 739
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Book Description
A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.
Author: Luc Devroye
Publisher: Springer Science & Business Media
ISBN: 1461386438
Category : Mathematics
Languages : en
Pages : 859
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Book Description
Thls text ls about one small fteld on the crossroads of statlstlcs, operatlons research and computer sclence. Statistleians need random number generators to test and compare estlmators before uslng them ln real l fe. In operatlons research, random numbers are a key component ln arge scale slmulatlons. Computer sclen tlsts need randomness ln program testlng, game playlng and comparlsons of algo rlthms. The appl catlons are wlde and varled. Yet all depend upon the same com puter generated random numbers. Usually, the randomness demanded by an appl catlon has some bullt-ln structure: typlcally, one needs more than just a sequence of Independent random blts or Independent uniform 0,1] random vari ables. Some users need random variables wlth unusual densltles, or random com blnatorlal objects wlth speclftc propertles, or random geometrlc objects, or ran dom processes wlth weil deftned dependence structures. Thls ls preclsely the sub ject area of the book, the study of non-uniform random varlates. The plot evolves around the expected complexlty of random varlate genera tlon algorlthms. We set up an ldeal zed computatlonal model (wlthout overdolng lt), we lntroduce the notlon of unlformly bounded expected complexlty, and we study upper and lower bounds for computatlonal complexlty. In short, a touch of computer sclence ls added to the fteld. To keep everythlng abstract, no tlmlngs or computer programs are lncluded. Thls was a Iabor of Iove. George Marsagl a created CS690, a course on ran dom number generat on at the School of Computer Sclence of McG ll Unlverslty."
Author: Geoffrey Grimmett
Publisher:
ISBN: 0198847602
Category : Mathematics
Languages : en
Pages : 682
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Book Description
Probability is a core topic in science and life. This successful self-contained volume leads the reader from the foundations of probability theory and random processes to advanced topics and it presents a mathematical treatment with many applications to real-life situations.
Author: Steven Kay
Publisher: Springer Science & Business Media
ISBN: 0387241582
Category : Technology & Engineering
Languages : en
Pages : 838
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Book Description
Intuitive Probability and Random Processes using MATLAB® is an introduction to probability and random processes that merges theory with practice. Based on the author’s belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are: *heavy reliance on computer simulation for illustration and student exercises *the incorporation of MATLAB programs and code segments *discussion of discrete random variables followed by continuous random variables to minimize confusion *summary sections at the beginning of each chapter *in-line equation explanations *warnings on common errors and pitfalls *over 750 problems designed to help the reader assimilate and extend the concepts Intuitive Probability and Random Processes using MATLAB® is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book. About the Author Steven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing. He has received the Education Award "for outstanding contributions in education and in writing scholarly books and texts..." from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering.
Author: J. Cacko
Publisher: Elsevier
ISBN: 0444598030
Category : Technology & Engineering
Languages : en
Pages : 245
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Book Description
This book covers the basic topics associated with the measurement, analysis and simulation of random environmental processes which are encountered in practice when dealing with the dynamics, fatigue and reliability of structures in real environmental conditions. The treatment is self-contained and the authors have brought together and integrated the most important information relevant to this topic in order that the newcomer can see and study it as a whole. This approach should also be of interest to experienced engineers from fatigue laboratories who want to learn more about the possible methods of simulation, especially for use in real time on electrohydraulic computer-controlled loading machines.Problems of constructing a measuring system are dealt with in the first chapter. Here the authors discuss the choice of measuring conditions and locations, as well as the organization of a chain of devices for measuring and recording random environmental processes. Some experience gained from practical measurements is also presented. The recorded processes are further analysed by various methods. The choice is governed by the aims of the measurements and applications of the results. Chapter 2 is thus devoted to methods of random process evaluations for digital computers, both from the fatigue and dynamic point of view. The most important chapter is Chapter 3 as this presents a review of up-to-date methods of random process simulation with given statistical characteristics. These methods naturally follow those of random process analysis, and their results form initial data for the corresponding simulations algorithms, including occurrences of characteristic parameters of counting methods, reproduction of correlation theory characteristics and of autoregressive models. The simulation of non-stationary processes is treated in depth, taking into account their importance for practical applications and also the lack of information of this subject.The book is intended to help resolve many practical problems concerning the methods and quality of environmental process evaluation and simulation which can arise when up-to-date loading systems with computer control are being used in material, component and structural fatigue and dynamic research.
Author: X. Rong Li
Publisher: CRC Press
ISBN: 1351421522
Category : Technology & Engineering
Languages : en
Pages : 472
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Book Description
With this innovative text, the study-and teaching- of probability and random signals becomes simpler, more streamlined, and more effective. Its unique "textgraph" format makes it both student-friendly and instructor-friendly. Pages with a larger typeface form a concise text for basic topics and make ideal transparencies; pages with smaller type provide more detailed explanations and more advanced material.
Author: Hisashi Kobayashi
Publisher: Cambridge University Press
ISBN: 1139502611
Category : Technology & Engineering
Languages : en
Pages : 813
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Book Description
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
