Böcker i Chapman & Hall/CRC Monographs on Statistics and Applied Probability-serien

Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics.

This book introduces the authors¿ recently developed approach to inference: the inferential model (IM) framework. This logical framework for exact probabilistic inference does not require the user to input prior information. The book covers the foundational motivations for this new approach, the basic theory behind its calibration properties, many important applications, and new directions for research. It explores a new way of thinking compared to existing schools of thought on statistical inference and encourages readers to think carefully about the correct approach to scientific inference.

This monograph presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, the authors study Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs). They explain how covariances are related to RKHSs and examine the Bayes¿ formula, the filtering and analytic problem related to fractional Brownian motion, and equivalence and singularity of Gaussian random fields. The book also describes applications in finance and spatial statistics and presents results on Dirichlet forms and associated Markov processes.

Exploring the advantages of the state-space approach, this book presents numerous computational procedures that can be applied to a previously specified linear model in state-space form. It discusses model estimation and signal extraction; describes many procedures to combine, decompose, aggregate, and disaggregate a state-space form; and covers the connection between mainstream time series models and the state-space representation. Source code, a complete user manual, and other materials related to the authors¿ MATLAB® toolbox are available on a supplementary website.

This book addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. It shows how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data. The book presents several extensions to the standard autoregressive model and other novel material developed by the authors that has not been published elsewhere. Data sets, MATLAB® code, and additional material are available on a supplementary website.

This book provides broad, up-to-date coverage of the Pareto model and its extensions. This edition expands several chapters to accommodate recent results and reflect the increased use of more computer-intensive inference procedures. It includes new material on multivariate inequality and new discussions of bivariate and multivariate income and survival models. This edition also explores recent ways of handling the problems of inference for Pareto models and their generalizations and extensions.

This book covers the theoretical developments and applications of sequential hypothesis testing and sequential quickest changepoint detection in a wide range of engineering and environmental domains. It reviews recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They treat conventional i.i.d. and general non-i.i.d. stochastic models in detail, including Markov, hidden Markov, state-space, regression, and autoregression models.

This book covers recent advances in the field, including vine copula modeling of high-dimensional data. The author develops vine copula models and generalizations, discusses other multivariate constructions and parametric copula families, and presents dependence and tail properties to assist readers in copula model selection. He also covers inference, diagnostics, model comparison, numerical methods, and algorithms for copula applications. Software and code area available on the author¿s website.

This book provides one of the first accounts of statistical analysis and inference based on approximate models Developed by the author, this approach consistently treats models as approximations to data, not to some underlying truth. The author develops a concept of approximation for probability models with applications to discrete data, location scale, ANOVA, nonparametric regression, image analysis, densities, time series, and model choice. He also offers a critique of statistics that covers likelihood, Bayesian statistics, sufficient statistics, efficiency, asymptotics, and model choice.

More than twice the size of its predecessor, this second edition reflects the major growth in spatial statistics as both a research area and an area of application. This edition includes four new chapters on spatial point patterns, big data, spatial and spatiotemporal gradient modeling, and the theoretical aspects of point-referenced modeling. It also expands several other chapters, updates the WinBUGS programs and R packages, doubles the number of exercises, and integrates many more color figures throughout the text.

This book shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIMs. He covers a range of PIMs, including models for misclassified data and models involving instrumental variables. He also includes real data applications of PIMs that have recently appeared in the literature.

Retaining all the material from the second edition and adding substantial new material, this third edition presents models and statistical methods for analyzing spatially referenced point process data. Reflected in the title, this edition now covers spatio-temporal point patterns. It also incorporates the use of R through several packages dedicated to the analysis of spatial point process data, with code and data sets available online. Practical examples illustrate how the methods are applied to analyze spatial data in the life sciences.

"Business, government, and industry all need efficient and accurate methods of summarizing and extracting information from the huge amounts of data collected and stored electronically. Thoroughly updated, the second edition of this popular text presents graphical and clustering methods.

Intended for academic statisticians, this book text such topics as: exact methods, with permutation techniques as the main unifying theme; estimating equations; and asymptotic approximations, particularly in the estimation of parameters in a general linear model.

Concentrates on diagnostic checking methods for stationary time series. With explanations and a focus firmly on applications, this book covers a range of different linear and nonlinear models, from various ARMA, and bilinear models to conditional non-Gaussian and ARCH models.

A collection of vignettes that examines statistics. It covers major areas of application and discusses theory and methods.

Offers a comprehensive development of a general theory of martingales indexed by a family of sets. This work establishes an appropriate framework that provides a suitable structure for a theory of martingales, developed from first principles, with enough generality to include many interesting examples.

Focuses on the various semiparametric methods in model estimation, specification testing, and selection of time series data. This book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data.

Examines survival analysis models and explores areas of accelerated life testing usually only touched upon in the literature. This book focuses with time-varying explanatory variables and to methods of semiparametric estimation. It includes goodness-of-fit tests for the important models.

Discusses the asymptotic theory of semimartingales needed for researchers working in the area of statistical inference for stochastic processes. This book covers topics that include: asymptotic likelihood theory, quasi-likelihood, likelihood and efficiency, inference for counting processes, and inference for semimartingale regression models.

The seventh volume in the SemStat series, this book presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible both to new students and seasoned researchers, each chapter starts with introductions to the topics and builds gradually toward discussing recent research. Chapters are self-contained and written by leading researchers from the field. The book includes applications to finance and econometrics and provides relevant software where applicable.

In the last twenty years, dynamic prediction models have been extensively used to monitor patient prognosis in survival analysis. Written by one of the pioneers in the area, this book synthesizes these developments in a unified framework. It covers a range of models, including prognostic and dynamic prediction of survival using genomic data and time-dependent information. The text includes numerous examples using real data taken from the authors¿ collaborative research. R programs are provided for implementing the methods.

Extreme value theory (EVT) provides tools for assessing risk of highly unusual developments, such as financial market crashes. This book presents a synthesis of recent research, with emphasis on dependent observations. It concentrates on modern topics, such as compound Poisson approximation, processes of exceedances, and nonparametric estimation methods, which have not been focused on in other books on extremes. Along with examples from finance and insurance that illustrate the methods, the book includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text.

Presents an overview of likelihood methods for the analysis of sample survey data, providing useful background material on likelihood inference. This book covers on a range of data types, including multilevel and aggregate data.

This book presents the first comprehensive and modern mathematical treatment of these mean field particle models, including refined convergence analysis on nonlinear Markov chain models. It also covers applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology.