Hilbert Space Methods in Probability and Statistical Inference

Foundations of Risk Analysis presents the issues core to risk analysis – understanding what risk means, expressing risk, building risk models, addressing uncertainty, and applying probability models to real problems. The author provides the readers with the knowledge and basic thinking they require to successfully manage risk and uncertainty to support decision making. This updated edition reflects recent developments on risk and uncertainty concepts, representations and treatment. New material in Foundations of Risk Analysis includes: An up to date presentation of how to understand, define and describe risk based on research carried out in recent years. A new definition of the concept of vulnerability consistent with the understanding of risk. Reflections on the need for seeing beyond probabilities to measure/describe uncertainties. A presentation and discussion of a method for assessing the importance of assumptions (uncertainty factors) in the background knowledge that the subjective probabilities are based on A brief introduction to approaches that produce interval (imprecise) probabilities instead of exact probabilities. In addition the new version provides a number of other improvements, for example, concerning the use of cost-benefit analyses and the As Low As Reasonably Practicable (ALARP) principle. Foundations of Risk Analysis provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty.

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: – On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; – Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; – Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.

Presents a useful new technique for analyzing the extreme-value behaviour of random fields Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on the analytical approximations of the statistical significance of extreme values. Several relatively complex applications of the technique to problems that emerge in practical situations are presented. All the examples are difficult to analyze using classical methods, and as a result, the author presents a novel technique, designed to be more accessible to the user. Extreme value analysis is widely applied in areas such as operational research, bioinformatics, computer science, finance and many other disciplines. This book will be useful for scientists, engineers and advanced graduate students who need to develop their own statistical tools for the analysis of their data. Whilst this book may not provide the reader with the specific answer it will inspire them to rethink their problem in the context of random fields, apply the method, and produce a solution.

Mixed modelling is very useful, and easier than you think! Mixed modelling is now well established as a powerful approach to statistical data analysis. It is based on the recognition of random-effect terms in statistical models, leading to inferences and estimates that have much wider applicability and are more realistic than those otherwise obtained. Introduction to Mixed Modelling leads the reader into mixed modelling as a natural extension of two more familiar methods, regression analysis and analysis of variance. It provides practical guidance combined with a clear explanation of the underlying concepts. Like the first edition, this new edition shows diverse applications of mixed models, provides guidance on the identification of random-effect terms, and explains how to obtain and interpret best linear unbiased predictors (BLUPs). It also introduces several important new topics, including the following: Use of the software SAS, in addition to GenStat and R. Meta-analysis and the multiple testing problem. The Bayesian interpretation of mixed models. Including numerous practical exercises with solutions, this book provides an ideal introduction to mixed modelling for final year undergraduate students, postgraduate students and professional researchers. It will appeal to readers from a wide range of scientific disciplines including statistics, biology, bioinformatics, medicine, agriculture, engineering, economics, archaeology and geography. Praise for the first edition: “One of the main strengths of the text is the bridge it provides between traditional analysis of variance and regression models and the more recently developed class of mixed models…Each chapter is well-motivated by at least one carefully chosen example…demonstrating the broad applicability of mixed models in many different disciplines…most readers will likely learn something new, and those previously unfamiliar with mixed models will obtain a solid foundation on this topic.”—Kerrie Nelson University of South Carolina, in American Statistician, 2007

This book grew out of an online interactive offered through statcourse.com, and it soon became apparent to the author that the course was too limited in terms of time and length in light of the broad backgrounds of the enrolled students. The statisticians who took the course needed to be brought up to speed both on the biological context as well as on the specialized statistical methods needed to handle large arrays. Biologists and physicians, even though fully knowledgeable concerning the procedures used to generate microaarrays, EEGs, or MRIs, needed a full introduction to the resampling methods—the bootstrap, decision trees, and permutation tests, before the specialized methods applicable to large arrays could be introduced. As the intended audience for this book consists both of statisticians and of medical and biological research workers as well as all those research workers who make use of satellite imagery including agronomists and meteorologists, the book provides a step-by-step approach to not only the specialized methods needed to analyze the data from microarrays and images, but also to the resampling methods, step-down multi-comparison procedures, multivariate analysis, as well as data collection and pre-processing. While many alternate techniques for analysis have been introduced in the past decade, the author has selected only those techniques for which software is available along with a list of the available links from which the software may be purchased or downloaded without charge. Topical coverage includes: very large arrays; permutation tests; applying permutation tests; gathering and preparing data for analysis; multiple tests; bootstrap; applying the bootstrap; classification methods; decision trees; and applying decision trees.