Hidden Markov Models for Time Series

An Introduction Using R, Second Edition

Author: Walter Zucchini,Iain L. MacDonald,Roland Langrock

Publisher: CRC Press

ISBN: 1482253844

Category: Mathematics

Page: 370

View: 9937

Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture–recapture data

Hidden Markov Models for Time Series

An Introduction Using R, Second Edition

Author: Walter Zucchini,Iain L. MacDonald,Roland Langrock

Publisher: CRC Press

ISBN: 1315355205

Category: Mathematics

Page: 370

View: 3520

Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture–recapture data

Hidden Markov Models for Time Series

An Introduction Using R

Author: Walter Zucchini,Iain L. MacDonald

Publisher: CRC Press

ISBN: 9781420010893

Category: Mathematics

Page: 288

View: 7465

Reveals How HMMs Can Be Used as General-Purpose Time Series Models Implements all methods in R Hidden Markov Models for Time Series: An Introduction Using R applies hidden Markov models (HMMs) to a wide range of time series types, from continuous-valued, circular, and multivariate series to binary data, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out computations for parameter estimation, model selection and checking, decoding, and forecasting. Illustrates the methodology in action After presenting the simple Poisson HMM, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference. Through examples and applications, the authors describe how to extend and generalize the basic model so it can be applied in a rich variety of situations. They also provide R code for some of the examples, enabling the use of the codes in similar applications. Effectively interpret data using HMMs This book illustrates the wonderful flexibility of HMMs as general-purpose models for time series data. It provides a broad understanding of the models and their uses.

Inference in Hidden Markov Models

Author: Olivier Cappé,Eric Moulines,Tobias Ryden

Publisher: Springer Science & Business Media

ISBN: 0387289828

Category: Mathematics

Page: 653

View: 4867

This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.

Statistical Methods for Spatio-Temporal Systems

Author: Barbel Finkenstadt,Leonhard Held,Valerie Isham

Publisher: CRC Press

ISBN: 1420011057

Category: Mathematics

Page: 286

View: 8886

Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time covariance functions. The contributors then describe stochastic and statistical models that are used to generate simulated rainfall sequences for hydrological use, such as flood risk assessment. The final chapter explores Gaussian Markov random field specifications and Bayesian computational inference via Gibbs sampling and Markov chain Monte Carlo, illustrating the methods with a variety of data examples, such as temperature surfaces, dioxin concentrations, ozone concentrations, and a well-established deterministic dynamical weather model.

Hidden Markov Models

Estimation and Control

Author: Robert J Elliott,Lakhdar Aggoun,John B. Moore

Publisher: Springer Science & Business Media

ISBN: 0387848541

Category: Science

Page: 382

View: 2135

As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.

Dynamic Linear Models with R

Author: Giovanni Petris,Sonia Petrone,Patrizia Campagnoli

Publisher: Springer Science & Business Media

ISBN: 0387772383

Category: Mathematics

Page: 252

View: 5467

State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used. A final chapter covers modern sequential Monte Carlo algorithms. The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.

State-Space Methods for Time Series Analysis

Theory, Applications and Software

Author: Jose Casals,Alfredo Garcia-Hiernaux,Miguel Jerez,Sonia Sotoca,A. Alexandre Trindade

Publisher: CRC Press

ISBN: 1482219603

Category: Mathematics

Page: 270

View: 6203

The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values. Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form. After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables. Web Resource The authors’ E4 MATLAB® toolbox offers all the computational procedures, administrative and analytical functions, and related materials for time series analysis. This flexible, powerful, and free software tool enables readers to replicate the practical examples in the text and apply the procedures to their own work.

Bayesian Programming

Author: Pierre Bessiere,Emmanuel Mazer,Juan Manuel Ahuactzin,Kamel Mekhnacha

Publisher: CRC Press

ISBN: 1439880336

Category: Business & Economics

Page: 380

View: 9890

Probability as an Alternative to Boolean Logic While logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain Data Emphasizing probability as an alternative to Boolean logic, Bayesian Programming covers new methods to build probabilistic programs for real-world applications. Written by the team who designed and implemented an efficient probabilistic inference engine to interpret Bayesian programs, the book offers many Python examples that are also available on a supplementary website together with an interpreter that allows readers to experiment with this new approach to programming. Principles and Modeling Only requiring a basic foundation in mathematics, the first two parts of the book present a new methodology for building subjective probabilistic models. The authors introduce the principles of Bayesian programming and discuss good practices for probabilistic modeling. Numerous simple examples highlight the application of Bayesian modeling in different fields. Formalism and Algorithms The third part synthesizes existing work on Bayesian inference algorithms since an efficient Bayesian inference engine is needed to automate the probabilistic calculus in Bayesian programs. Many bibliographic references are included for readers who would like more details on the formalism of Bayesian programming, the main probabilistic models, general purpose algorithms for Bayesian inference, and learning problems. FAQs Along with a glossary, the fourth part contains answers to frequently asked questions. The authors compare Bayesian programming and possibility theories, discuss the computational complexity of Bayesian inference, cover the irreducibility of incompleteness, and address the subjectivist versus objectivist epistemology of probability. The First Steps toward a Bayesian Computer A new modeling methodology, new inference algorithms, new programming languages, and new hardware are all needed to create a complete Bayesian computing framework. Focusing on the methodology and algorithms, this book describes the first steps toward reaching that goal. It encourages readers to explore emerging areas, such as bio-inspired computing, and develop new programming languages and hardware architectures.

Finite Mixture and Markov Switching Models

Author: Sylvia Frühwirth-Schnatter

Publisher: Springer Science & Business Media

ISBN: 0387357688

Category: Mathematics

Page: 494

View: 7193

The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Hidden Semi-Markov Models

Theory, Algorithms and Applications

Author: Shun-Zheng Yu

Publisher: Morgan Kaufmann

ISBN: 0128027711

Category: Computers

Page: 208

View: 9919

Hidden semi-Markov models (HSMMs) are among the most important models in the area of artificial intelligence / machine learning. Since the first HSMM was introduced in 1980 for machine recognition of speech, three other HSMMs have been proposed, with various definitions of duration and observation distributions. Those models have different expressions, algorithms, computational complexities, and applicable areas, without explicitly interchangeable forms. Hidden Semi-Markov Models: Theory, Algorithms and Applications provides a unified and foundational approach to HSMMs, including various HSMMs (such as the explicit duration, variable transition, and residential time of HSMMs), inference and estimation algorithms, implementation methods and application instances. Learn new developments and state-of-the-art emerging topics as they relate to HSMMs, presented with examples drawn from medicine, engineering and computer science. Discusses the latest developments and emerging topics in the field of HSMMs Includes a description of applications in various areas including, Human Activity Recognition, Handwriting Recognition, Network Traffic Characterization and Anomaly Detection, and Functional MRI Brain Mapping. Shows how to master the basic techniques needed for using HSMMs and how to apply them.

Hidden Markov and Other Models for Discrete- valued Time Series

Author: Iain L. MacDonald,Walter Zucchini

Publisher: CRC Press

ISBN: 9780412558504

Category: Mathematics

Page: 256

View: 3187

Discrete-valued time series are common in practice, but methods for their analysis are not well-known. In recent years, methods have been developed which are specifically designed for the analysis of discrete-valued time series. Hidden Markov and Other Models for Discrete-Valued Time Series introduces a new, versatile, and computationally tractable class of models, the "hidden Markov" models. It presents a detailed account of these models, then applies them to data from a wide range of diverse subject areas, including medicine, climatology, and geophysics. This book will be invaluable to researchers and postgraduate and senior undergraduate students in statistics. Researchers and applied statisticians who analyze time series data in medicine, animal behavior, hydrology, and sociology will also find this information useful.

Statistical Learning with Sparsity

The Lasso and Generalizations

Author: Trevor Hastie,Robert Tibshirani,Martin Wainwright

Publisher: CRC Press

ISBN: 1498712177

Category: Business & Economics

Page: 367

View: 9994

Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of l1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

Multistate Models for the Analysis of Life History Data

Author: Richard J Cook,Jerald F. Lawless

Publisher: CRC Press

ISBN: 1351646052

Category: Mathematics

Page: 440

View: 1546

Multistate Models for the Analysis of Life History Data provides the first comprehensive treatment of multistate modeling and analysis, including parametric, nonparametric and semiparametric methods applicable to many types of life history data. Special models such as illness-death, competing risks and progressive processes are considered, as well as more complex models. The book provides both theoretical development and illustrations of analysis based on data from randomized trials and observational cohort studies in health research. Features Discusses a wide range of applications of multistate models Presents methods for both continuously and intermittently observed life history processes Gives a thorough discussion of conditionally independent censoring and observation processes Discusses models with random effects and joint models for two or more multistate processes Discusses and illustrates software for multistate analysis that is available in R Target audience includes those engaged in research and applications involving multistate models Richard Cook is Canada Research Chair in Statistical Methods for Health Research at the University of Waterloo. He has received the Gold Medal of the Statistical Society of Canada and is a Fellow of the American Statistical Association. He collaborates and consults widely on health research and has given many short courses. He and Dr. Lawless previously coauthored the influential book, The Statistical Analysis of Recurrent Events (Springer, 2007). Jerald Lawless is Distinguished Professor Emeritus at the University of Waterloo. He is a Fellow of the Royal Society of Canada, a Gold Medal recipient of the Statistical Society of Canada and Fellow of the American Statistical Association. He is a past editor of Technometrics and has collaborated and consulted in numerous areas. He has presented many short courses, with Dr. Cook and individually. "The authors of the book are internationally renowned experts in the field of multi-state modeling and have written an extremely clear and comprehensive book on the topic that covers many different aspects, from the fundamental theory to the practical side of analyzing data and interpreting results. The examples are well chosen to represent the most common types of multi-state processes that public health researchers could encounter. The inclusion of software code to illustrate how the models can be fit and interpreted is especially helpful to readers." (Mimi Kim, Albert Einstein College of Medicine)

Bayesian Networks in R

with Applications in Systems Biology

Author: Radhakrishnan Nagarajan,Marco Scutari,Sophie Lèbre

Publisher: Springer Science & Business Media

ISBN: 1461464463

Category: Computers

Page: 157

View: 1714

Bayesian Networks in R with Applications in Systems Biology is unique as it introduces the reader to the essential concepts in Bayesian network modeling and inference in conjunction with examples in the open-source statistical environment R. The level of sophistication is also gradually increased across the chapters with exercises and solutions for enhanced understanding for hands-on experimentation of the theory and concepts. The application focuses on systems biology with emphasis on modeling pathways and signaling mechanisms from high-throughput molecular data. Bayesian networks have proven to be especially useful abstractions in this regard. Their usefulness is especially exemplified by their ability to discover new associations in addition to validating known ones across the molecules of interest. It is also expected that the prevalence of publicly available high-throughput biological data sets may encourage the audience to explore investigating novel paradigms using the approaches presented in the book.

Nonlinear Time Series

Theory, Methods and Applications with R Examples

Author: Randal Douc,Eric Moulines,David Stoffer

Publisher: CRC Press

ISBN: 1466502347

Category: Mathematics

Page: 551

View: 4318

Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models—without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes. The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods. The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently. Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.

Survival and Event History Analysis

A Process Point of View

Author: Odd Aalen,Ornulf Borgan,Hakon Gjessing

Publisher: Springer Science & Business Media

ISBN: 038768560X

Category: Mathematics

Page: 540

View: 4813

The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

Nonparametric Models for Longitudinal Data

With Implementation in R

Author: Colin O. Wu,Xin Tian

Publisher: CRC Press

ISBN: 0429939086

Category: Mathematics

Page: 552

View: 5036

Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: Provides an overview of parametric and semiparametric methods Shows smoothing methods for unstructured nonparametric models Covers structured nonparametric models with time-varying coefficients Discusses nonparametric shared-parameter and mixed-effects models Presents nonparametric models for conditional distributions and functionals Illustrates implementations using R software packages Includes datasets and code in the authors’ website Contains asymptotic results and theoretical derivations Both authors are mathematical statisticians at the National Institutes of Health (NIH) and have published extensively in statistical and biomedical journals. Colin O. Wu earned his Ph.D. in statistics from the University of California, Berkeley (1990), and is also Adjunct Professor at the Georgetown University School of Medicine. He served as Associate Editor for Biometrics and Statistics in Medicine, and reviewer for National Science Foundation, NIH, and the U.S. Department of Veterans Affairs. Xin Tian earned her Ph.D. in statistics from Rutgers, the State University of New Jersey (2003). She has served on various NIH committees and collaborated extensively with clinical researchers.

Introduction to Stochastic Processes, Second Edition

Author: Gregory F. Lawler

Publisher: CRC Press

ISBN: 9781584886518

Category: Mathematics

Page: 248

View: 8082

Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.