Bücher der Reihe Chapman & Hall/CRC Monographs on Statistics and Applied Probability

This text looks at data-analytic approaches to regression problems arising from many scientific disciplines. The aim of these methods is to relax assumptions on the form of a regression function and to let data search for a suitable function. The available data is also described.

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. The authors cover the lasso for linear regression, generali

Exploring the recent achievements that have occurred since the mid-1990s, this book explains how to use modern algorithms to fit geometric contours to observed data in image processing and computer vision. The author covers all facets-geometric, statistical, and computational-of the methods. He looks at how the numerical algorithms relate to one

This book provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It attempts to establish a gold standard for how a statistical analysis should proceed. The book illustrates relative belief theory using many examples and describes the strengths and weaknesses of the theory. Th

Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account

This is the second edition of a monograph on generalized linear models with random effects that extends the classic work of McCullagh and Nelder. It has been thoroughly updated, with around 80 pages added, including new material on the extended likelihood approach that strengthens the theoretical basis of the methodology, new developments in var

This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.

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.

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.

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.

This volume describes methods for the analysis of relations between a set of variables, with the emphasis mainly on observational studies in the social sciences. Also examined is the role of intermediate variables serving as responses to some variables and as explanatory to others.

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.

Since the 1930s, basic statistical problems have been formulated not in terms of interpreting data as evidence but in terms of choosing between alternative courses of action. This monograph is about the problem of representing and interpreting data as evidence.

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.

Deals with the techniques for fitting and choosing models that are linear in their parameters and to understanding and correcting the bias introduced by selecting a model. This title includes a chapter on Bayesian methods and an example from the field of near infrared spectroscopy. It emphasises on cross-validation and focuses on bootstrapping.

Providing a toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics.

Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. Nonparametric regression and density estimation are two of the most fundamental problems to which kernel smoothing provides a simple and effective solution.

This book describes the properties of stochastic probabilistic models and develops the applied mathematics of stochastic point processes. It is useful to students and research workers in probability and statistics and also to research workers wishing to apply stochastic point processes.

Introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. This book offers an introduction to Grobner bases and a description of their applications to experimental design.

..."by far the best book on its topic." -International Statistical Reveiw

Gaussian Markov Random Field (GMRF) models, most widely used in spatial statistics are presented in this, the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects.

This text describes methods for the analysis of relationships between a set a variables, with emphasis largely, but not entirely on observational studies in the social sciences.

A revised textbook covering all aspects of risk theory in a practical way. It follows on from the late R.E. Beard's book "Risk Theory" and should be of interest to actuarial students and practitioners working in the insurance industry as well as economists and applied statisticians.

Helps researchers understand the theory of the design of experiments so they can easily adapt general principles to their specialties. This book brings the theory to non-statisticians at a reasonable mathematical level so that they can apply and adapt the special designs.

Offers a description of singular spectrum analysis (SSA) general theory and methodology. This book introduces the basic concepts and presents a detailed treatment of the methodology. It covers the theory of SSA. It offers an opportunity to obtain a working knowledge of why, when, and how SSA works.

Quantal response (or dose-response) data arise in many areas, both through experimental and observational studies. Particular emphasis is placed in this book on applications in bioassay and toxicology. Throughout, the material is motivated by a range of practical examples.

A survey of recent methodology regarding the statistical analysis and detection of defective items in various types of inspection for attributes, when the inspection itself is subject to error. The book covers both theory and practice, with an emphasis on group testing.

A variety of power tools for data analysis, based on non-parametric regression or smoothing techniques, are described in this text. These methods relax the usual linear assumption in many standard models, allowing the analyst to uncover structure in data.