The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering.

Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statistics.

Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians. This new edition has been revised towards a coherent and flowing coverage of these simulation techniques, with incorporation of the most recent developments in the field. In particular, the introductory coverage of random variable generation has been totally revised, with many concepts being unified through a fundamental theorem of simulation.

This book serves as an advanced text for a graduate course on stochastic algorithms for the students of probability and statistics, engineering, economics and machine learning. This second edition gives a comprehensive treatment of stochastic approximation algorithms based on the ordinary differential equation (ODE) approach which analyses the algorithm in terms of a limiting ODE. It has a streamlined treatment of the classical convergence analysis and includes several recent developments such as concentration bounds, avoidance of traps, stability tests, distributed and asynchronous schemes, multiple time scales, general noise models, etc., and a category-wise exposition of many important applications. It is also a useful reference for researchers and practitioners in the field.

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov­ ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil­ ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Written by a leading researcher this book presents an introduction to Stochastic Petri Nets covering the modeling power of the proposed SPN model, the stability conditions and the simulation methods. Its unique and well-written approach provides a timely and important addition to the literature. Appeals to a wide range of researchers in engineering, computer science, mathematics and OR.

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. These include: * the setting of learning problems based on the model of minimizing the risk functional from empirical data * a comprehensive analysis of the empirical risk minimization principle including necessary and sufficient conditions for its consistency * non-asymptotic bounds for the risk achieved using the empirical risk minimization principle * principles for controlling the generalization ability of learning machines using small sample sizes based on these bounds * the Support Vector methods that control the generalization ability when estimating function using small sample size.

Robust statistical methods are now being used in a wide range of disciplines. The appeal of these methods is that they are designed to perform about as well as classic techniques when standard assumptions are true—but they continue to perform well in situations where classic methods perform poorly.

This textbook covers the fundamentals of statistical inference and statistical theory including Bayesian and frequentist approaches and methodology possible without excessive emphasis on the underlying mathematics. This book is about some of the basic principles of statistics that are necessary to understand and evaluate methods for analyzing complex data sets. The likelihood function is used for pure likelihood inference throughout the book. There is also coverage of severity and finite population sampling. The material was developed from an introductory statistical theory course taught by the author at the Johns Hopkins University’s Department of Biostatistics. Students and instructors in public health programs will benefit from the likelihood modeling approach that is used throughout the text. This will also appeal to epidemiologists and psychometricians. After a brief introduction, there are chapters on estimation, hypothesis testing, and maximum likelihood modeling. The book concludes with sections on Bayesian computation and inference. An appendix contains unique coverage of the interpretation of probability, and coverage of probability and mathematical concepts.

Most of the observable phenomena in the empirical sciences are of multivariate nature. This book presents the tools and concepts of multivariate data analysis with a strong focus on applications. The text is devided into three parts. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents from a theoretical point of view distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide basket of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.

An observational study is an empiric investigation of effects caused by treatments when randomized experimentation is unethical or infeasible. Observational studies are common in most fields that study the effects of treatments on people, including medicine, economics, epidemiology, education, psychology, political science and sociology. The quality and strength of evidence provided by an observational study is determined largely by its design. Design of Observational Studies is both an introduction to statistical inference in observational studies and a detailed discussion of the principles that guide the design of observational studies.

Time series and random ?elds are main topics in modern statistical techniques. They are essential for applications where randomness plays an important role. Indeed, physical constraints mean that serious modelling cannot be done - ing only independent sequences. This is a real problem because asymptotic properties are not always known in this case. Thepresentworkisdevotedtoprovidingaframeworkforthecommonlyused time series. In order to validate the main statistics, one needs rigorous limit theorems. In the ?eld of probability theory, asymptotic behavior of sums may or may not be analogous to those of independent sequences. We are involved with this ?rst case in this book. Very sharp results have been proved for mixing processes, a notion int- duced by Murray Rosenblatt [166]. Extensive discussions of this topic may be found in his Dependence in Probability and Statistics (a monograph published by Birkhau ¨ser in 1986) and in Doukhan (1994) [61], and the sharpest results may be found in Rio (2000)[161]. However, a counterexample of a really simple non-mixing process was exhibited by Andrews (1984) [2]. The notion of weak dependence discussed here takes real account of the available models, which are discussed extensively. Our idea is that robustness of the limit theorems with respect to the model should be taken into account. In real applications, nobody may assert, for example, the existence of a density for the inputs in a certain model, while such assumptions are always needed when dealing with mixing concepts.

Winner of the 2004 DeGroot Prize

This paperback edition, a reprint of the 2001 edition, is a graduate-level textbook that introduces Bayesian statistics and decision theory. It covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration including Gibbs sampling, and other MCMC techniques. It was awarded the 2004 DeGroot Prize by the International Society for Bayesian Analysis (ISBA) for setting "a new standard for modern textbooks dealing with Bayesian methods, especially those using MCMC techniques, and that it is a worthy successor to DeGroot's and Berger's earlier texts".

Thisbook,likemanyotherbooks,wasdeliveredundertremendousinspiration and encouragement from my teachers, research collaborators, and students. My interest in longitudinal data analysis began with a short course taught jointly by K. Y. Liang and S. L. Zeger at the Statistical Society of Canada Conference in Acadia University, Nova Scotia, in the spring of 1993. At that time, I was a ?rst-year PhD student in the Department of Statistics at the University of British Columbia, and was eagerly seeking potential topics for my PhD dissertation. It was my curiosity (driven largely by my terrible c- fusion) with the generalized estimating equations (GEEs) introduced in the short course that attracted me to the ?eld of correlated data analysis. I hope that my experience in learning about it has enabled me to make this book an enjoyable intellectual journey for new researchers entering the ?eld. Thus, the book aims at graduate students and methodology researchers in stat- tics or biostatistics who are interested in learning the theory and methods of correlated data analysis. I have attempted to give a systematic account of regression models and their applications to the modeling and analysis of correlated data. Longitu- nal data, as an important type of correlated data, has been used as a main venue for motivation, methodological development, and illustration throu- out the book. Given the many applied books on longitudinal data analysis - ready available, this book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications.

This is the first book to explain and demonstrate the tremendous ability of Pulse-Coupled Neural Networks (PCNNs) when applied to the field of image processing. PCNNs and their derivatives are biologically inspired models that are powerful tools for extracting texture, segments, and edges from images. As these attributes form the foundations of most image processing tasks, the use of PCNNs facilitates traditional tasks such as recognition, foveation, and image fusion. PCNN technology has also paved the way for new image processing techniques such as object isolation, spiral image fusion, image signatures, and content-based image searches. This volume contains examples of several image processing applications, as well as a review of hardware implementations.