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Sums And Gaussian Vectors
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Book Synopsis Sums and Gaussian Vectors by : Vadim Yurinsky
Download or read book Sums and Gaussian Vectors written by Vadim Yurinsky and published by Springer. This book was released on 2006-11-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Model-Based Signal Processing by : James V. Candy
Download or read book Model-Based Signal Processing written by James V. Candy and published by John Wiley & Sons. This book was released on 2005-10-27 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique treatment of signal processing using a model-based perspective Signal processing is primarily aimed at extracting useful information, while rejecting the extraneous from noisy data. If signal levels are high, then basic techniques can be applied. However, low signal levels require using the underlying physics to correct the problem causing these low levels and extracting the desired information. Model-based signal processing incorporates the physical phenomena, measurements, and noise in the form of mathematical models to solve this problem. Not only does the approach enable signal processors to work directly in terms of the problem's physics, instrumentation, and uncertainties, but it provides far superior performance over the standard techniques. Model-based signal processing is both a modeler's as well as a signal processor's tool. Model-Based Signal Processing develops the model-based approach in a unified manner and follows it through the text in the algorithms, examples, applications, and case studies. The approach, coupled with the hierarchy of physics-based models that the author develops, including linear as well as nonlinear representations, makes it a unique contribution to the field of signal processing. The text includes parametric (e.g., autoregressive or all-pole), sinusoidal, wave-based, and state-space models as some of the model sets with its focus on how they may be used to solve signal processing problems. Special features are provided that assist readers in understanding the material and learning how to apply their new knowledge to solving real-life problems. * Unified treatment of well-known signal processing models including physics-based model sets * Simple applications demonstrate how the model-based approach works, while detailed case studies demonstrate problem solutions in their entirety from concept to model development, through simulation, application to real data, and detailed performance analysis * Summaries provided with each chapter ensure that readers understand the key points needed to move forward in the text as well as MATLAB(r) Notes that describe the key commands and toolboxes readily available to perform the algorithms discussed * References lead to more in-depth coverage of specialized topics * Problem sets test readers' knowledge and help them put their new skills into practice The author demonstrates how the basic idea of model-based signal processing is a highly effective and natural way to solve both basic as well as complex processing problems. Designed as a graduate-level text, this book is also essential reading for practicing signal-processing professionals and scientists, who will find the variety of case studies to be invaluable. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department
Book Synopsis Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by : V.V. Buldygin
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.
Book Synopsis Model-Based Processing by : James V. Candy
Download or read book Model-Based Processing written by James V. Candy and published by John Wiley & Sons. This book was released on 2019-03-15 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bridge between the application of subspace-based methods for parameter estimation in signal processing and subspace-based system identification in control systems Model-Based Processing: An Applied Subspace Identification Approach provides expert insight on developing models for designing model-based signal processors (MBSP) employing subspace identification techniques to achieve model-based identification (MBID) and enables readers to evaluate overall performance using validation and statistical analysis methods. Focusing on subspace approaches to system identification problems, this book teaches readers to identify models quickly and incorporate them into various processing problems including state estimation, tracking, detection, classification, controls, communications, and other applications that require reliable models that can be adapted to dynamic environments. The extraction of a model from data is vital to numerous applications, from the detection of submarines to determining the epicenter of an earthquake to controlling an autonomous vehicles—all requiring a fundamental understanding of their underlying processes and measurement instrumentation. Emphasizing real-world solutions to a variety of model development problems, this text demonstrates how model-based subspace identification system identification enables the extraction of a model from measured data sequences from simple time series polynomials to complex constructs of parametrically adaptive, nonlinear distributed systems. In addition, this resource features: Kalman filtering for linear, linearized, and nonlinear systems; modern unscented Kalman filters; as well as Bayesian particle filters Practical processor designs including comprehensive methods of performance analysis Provides a link between model development and practical applications in model-based signal processing Offers in-depth examination of the subspace approach that applies subspace algorithms to synthesized examples and actual applications Enables readers to bridge the gap from statistical signal processing to subspace identification Includes appendices, problem sets, case studies, examples, and notes for MATLAB Model-Based Processing: An Applied Subspace Identification Approach is essential reading for advanced undergraduate and graduate students of engineering and science as well as engineers working in industry and academia.
Book Synopsis Signal Processing by : James Vincent Candy
Download or read book Signal Processing written by James Vincent Candy and published by John Wiley & Sons. This book was released on 2024-11-27 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separate signals from noise with this valuable introduction to signal processing by applied decomposition The decomposition of complex signals into their sub-signals or individual components is a crucial tool in signal processing. It allows each component of a signal to be analyzed individually and enables the signal to be isolated from noise and processed in full. Decomposition processes have not always been widely adopted due to the difficult underlying mathematics and complex applications. This text simplifies these obstacles. Signal Processing: An Applied Decomposition Approach demystifies these tools from a model-based perspective. This offers a mathematically informed, “step-by-step” analysis of the process by breaking down a composite signal/system into its constituent parts, while introducing both fundamental concepts and advanced applications. This comprehensive approach addresses each of the major decomposition techniques, making it an indispensable addition to any library specializing in signal processing. Signal Processing readers will find: Signal decomposition techniques developed from the data-based, spectral-based and model-based perspectives incorporate: statistical approaches (PCA, ICA, Singular Spectrum); spectral approaches (MTM, PHD, MUSIC); and model-based approaches (EXP, LATTICE, SSP) In depth discussion of topics includes signal/system estimation and decomposition, time domain and frequency domain techniques, systems theory, modal decompositions, applications and many more Numerous figures, examples, and tables illustrating key concepts and algorithms are developed throughout the text Includes problem sets, case studies, real-world applications as well as MATLAB notes highlighting applicable commands Signal Processing is ideal for engineering and scientific professionals, as well as graduate students seeking a focused text on signal/system decomposition with performance metrics and real-world applications.
Book Synopsis Fundamentals of Stochastic Signals, Systems and Estimation Theory with Worked Examples by : Branko Kovačević
Download or read book Fundamentals of Stochastic Signals, Systems and Estimation Theory with Worked Examples written by Branko Kovačević and published by . This book was released on 2008 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bayesian Signal Processing by : James V. Candy
Download or read book Bayesian Signal Processing written by James V. Candy and published by John Wiley & Sons. This book was released on 2016-06-20 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the Bayesian approach to statistical signal processing for a variety of useful model sets This book aims to give readers a unified Bayesian treatment starting from the basics (Baye’s rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on “Sequential Bayesian Detection,” a new section on “Ensemble Kalman Filters” as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to “fill-in-the gaps” of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical “sanity testing” lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theory metrics and their application to PF designs is fully developed and applied. These expansions of the book have been updated to provide a more cohesive discussion of Bayesian processing with examples and applications enabling the comprehension of alternative approaches to solving estimation/detection problems. The second edition of Bayesian Signal Processing features: “Classical” Kalman filtering for linear, linearized, and nonlinear systems; “modern” unscented and ensemble Kalman filters: and the “next-generation” Bayesian particle filters Sequential Bayesian detection techniques incorporating model-based schemes for a variety of real-world problems Practical Bayesian processor designs including comprehensive methods of performance analysis ranging from simple sanity testing and ensemble techniques to sophisticated information metrics New case studies on adaptive particle filtering and sequential Bayesian detection are covered detailing more Bayesian approaches to applied problem solving MATLAB® notes at the end of each chapter help readers solve complex problems using readily available software commands and point out other software packages available Problem sets included to test readers’ knowledge and help them put their new skills into practice Bayesian Signal Processing, Second Edition is written for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.
Book Synopsis Probability, Random Signals, and Statistics by : X. Rong Li
Download or read book Probability, Random Signals, and Statistics written by X. Rong Li and published by CRC Press. This book was released on 2017-12-14 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Concentration Inequalities by : Stéphane Boucheron
Download or read book Concentration Inequalities written by Stéphane Boucheron and published by Oxford University Press. This book was released on 2013-02-07 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.
Book Synopsis Probability Distributions Involving Gaussian Random Variables by : Marvin K. Simon
Download or read book Probability Distributions Involving Gaussian Random Variables written by Marvin K. Simon and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling. Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.
Book Synopsis Mathematical Perspectives on Neural Networks by : Paul Smolensky
Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky and published by Psychology Press. This book was released on 2013-05-13 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
Book Synopsis Probability, Random Variables, Statistics, and Random Processes by : Ali Grami
Download or read book Probability, Random Variables, Statistics, and Random Processes written by Ali Grami and published by John Wiley & Sons. This book was released on 2019-03-04 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book. The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 – 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 – 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 – 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 – 12), delves into the characterization and processing of random processes. Other notable features include: Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.
Book Synopsis Asymptotic Methods in Probability and Statistics with Applications by : N. Balakrishnan
Download or read book Asymptotic Methods in Probability and Statistics with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.
Book Synopsis Stochastic Processes by : Robert G. Gallager
Download or read book Stochastic Processes written by Robert G. Gallager and published by Cambridge University Press. This book was released on 2013-12-12 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.
Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio
Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.
Book Synopsis Introduction to Probability, Statistics, and Random Processes by : Hossein Pishro-Nik
Download or read book Introduction to Probability, Statistics, and Random Processes written by Hossein Pishro-Nik and published by . This book was released on 2014-08-15 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
