markov chains analytic and monte carlo computations wiley series in probability and statistics

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Markov Chains

Author : Carl Graham
ISBN : 9781118517079
Genre : Mathematics
File Size : 58. 38 MB
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Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies. A detailed and rigorous presentation of Markov chains with discrete time and state space. An appendix presenting probabilistic notions that are necessary to the reader, as well as giving more advanced measure-theoretic notions.

Markov Chains

Author : Carl Graham
ISBN : 9781118882696
Genre : Mathematics
File Size : 26. 11 MB
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Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies. A detailed and rigorous presentation of Markov chains with discrete time and state space. An appendix presenting probabilistic notions that are necessary to the reader, as well as giving more advanced measure-theoretic notions.

Time Series Analysis

Author : Wilfredo Palma
ISBN : 9781118634233
Genre : Mathematics
File Size : 52. 59 MB
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A modern and accessible guide to the analysis of introductory time series data Featuring an organized and self-contained guide, Time Series Analysis provides a broad introduction to the most fundamental methodologies and techniques of time series analysis. The book focuses on the treatment of univariate time series by illustrating a number of well-known models such as ARMA and ARIMA. Providing contemporary coverage, the book features several useful and newlydeveloped techniques such as weak and strong dependence, Bayesian methods, non-Gaussian data, local stationarity, missing values and outliers, and threshold models. Time Series Analysis includes practical applications of time series methods throughout, as well as: Real-world examples and exercise sets that allow readers to practice the presented methods and techniques Numerous detailed analyses of computational aspects related to the implementation of methodologies including algorithm efficiency, arithmetic complexity, and process time End-of-chapter proposed problems and bibliographical notes to deepen readers’ knowledge of the presented material Appendices that contain details on fundamental concepts and select solutions of the problems implemented throughout A companion website with additional data fi les and computer codes Time Series Analysis is an excellent textbook for undergraduate and beginning graduate-level courses in time series as well as a supplement for students in advanced statistics, mathematics, economics, finance, engineering, and physics. The book is also a useful reference for researchers and practitioners in time series analysis, econometrics, and finance. Wilfredo Palma, PhD, is Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. He has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. He is the author of Long-Memory Time Series: Theory and Methods, also published by Wiley.

Simulation And The Monte Carlo Method

Author : Reuven Y. Rubinstein
ISBN : 9781118210529
Genre : Mathematics
File Size : 20. 37 MB
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This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo Variance reduction techniques such as the transform likelihood ratio method and the screening method The score function method for sensitivity analysis The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization The cross-entropy method to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

Introduction To Time Series Analysis And Forecasting

Author : Douglas C. Montgomery
ISBN : 9781118745151
Genre : Mathematics
File Size : 47. 57 MB
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Praise for the First Edition "…[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both popular and modern time series methodologies as well as an introduction to Bayesian methods in forecasting. Introduction to Time Series Analysis and Forecasting, Second Edition also includes: Over 300 exercises from diverse disciplines including health care, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®, and R that illustrate the theory and practicality of forecasting techniques in the context of time-oriented data New material on frequency domain and spatial temporal data analysis Expanded coverage of the variogram and spectrum with applications as well as transfer and intervention model functions A supplementary website featuring PowerPoint® slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, Second Edition is an ideal textbook upper-undergraduate and graduate-levels courses in forecasting and time series. The book is also an excellent reference for practitioners and researchers who need to model and analyze time series data to generate forecasts.

Markov Chains

Author : Pierre Bremaud
ISBN : 9781475731248
Genre : Mathematics
File Size : 26. 8 MB
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Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

Monte Carlo Statistical Methods

Author : Christian Robert
ISBN : 9781475741452
Genre : Mathematics
File Size : 81. 94 MB
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We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

The Fitness Of Information

Author : Chaomei Chen
ISBN : 9781118594209
Genre : Mathematics
File Size : 89. 28 MB
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Theories and practices to assess critical information in a complex adaptive system Organized for readers to follow along easily, The Fitness of Information: Quantitative Assessments of Critical Evidence provides a structured outline of the key challenges in assessing crucial information in a complex adaptive system. Illustrating a variety of computational and explanatory challenges, the book demonstrates principles and practical implications of exploring and assessing the fitness of information in an extensible framework of adaptive landscapes. The book’s first three chapters introduce fundamental principles and practical examples in connection to the nature of aesthetics, mental models, and the subjectivity of evidence. In particular, the underlying question is how these issues can be addressed quantitatively, not only computationally but also explanatorily. The next chapter illustrates how one can reduce the level of complexity in understanding the structure and dynamics of scientific knowledge through the design and use of the CiteSpace system for visualizing and analyzing emerging trends in scientific literature. The following two chapters explain the concepts of structural variation and the fitness of information in a framework that builds on the idea of fitness landscape originally introduced to study population evolution. The final chapter presents a dual-map overlay technique and demonstrates how it supports a variety of analytic tasks for a new type of portfolio analysis. The Fitness of Information: Quantitative Assessments of Critical Evidence also features: In-depth case studies and examples that characterize far-reaching concepts, illustrate underlying principles, and demonstrate profound challenges and complexities at various levels of analytic reasoning Wide-ranging topics that underline the common theme, from the subjectivity of evidence in criminal trials to detecting early signs of critical transitions and mechanisms behind radical patents An extensible and unifying framework for visual analytics by transforming analytic reasoning tasks to the assessment of critical evidence The Fitness of Information: Quantitative Assessments of Critical Evidence is a suitable reference for researchers, analysts, and practitioners who are interested in analyzing evidence and making decisions with incomplete, uncertain, and even conflicting information. The book is also an excellent textbook for upper-undergraduate and graduate-level courses on visual analytics, information visualization, and business analytics and decision support systems.

Advanced Markov Chain Monte Carlo Methods

Author : Faming Liang
ISBN : 9780470669730
Genre : Mathematics
File Size : 68. 71 MB
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Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.

Probabilistic Finite Element Model Updating Using Bayesian Statistics

Author : Tshilidzi Marwala
ISBN : 9781119153009
Genre : Technology & Engineering
File Size : 28. 85 MB
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Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to Aeronautical and Mechanical Engineering Tshilidzi Marwala and Ilyes Boulkaibet, University of Johannesburg, South Africa Sondipon Adhikari, Swansea University, UK Covers the probabilistic finite element model based on Bayesian statistics with applications to aeronautical and mechanical engineering Finite element models are used widely to model the dynamic behaviour of many systems including in electrical, aerospace and mechanical engineering. The book covers probabilistic finite element model updating, achieved using Bayesian statistics. The Bayesian framework is employed to estimate the probabilistic finite element models which take into account of the uncertainties in the measurements and the modelling procedure. The Bayesian formulation achieves this by formulating the finite element model as the posterior distribution of the model given the measured data within the context of computational statistics and applies these in aeronautical and mechanical engineering. Probabilistic Finite Element Model Updating Using Bayesian Statistics contains simple explanations of computational statistical techniques such as Metropolis-Hastings Algorithm, Slice sampling, Markov Chain Monte Carlo method, hybrid Monte Carlo as well as Shadow Hybrid Monte Carlo and their relevance in engineering. Key features: Contains several contributions in the area of model updating using Bayesian techniques which are useful for graduate students. Explains in detail the use of Bayesian techniques to quantify uncertainties in mechanical structures as well as the use of Markov Chain Monte Carlo techniques to evaluate the Bayesian formulations. The book is essential reading for researchers, practitioners and students in mechanical and aerospace engineering.

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