Bücher der Reihe Cambridge Series in Statistical and Probabilistic Mathematics

Bootstrap methods enable fairly sophisticated statistical calculations to be done by computer simulation. The range of application is broad: from biology and medicine through to econometrics and finance. Compared with other treatments, applications are thoroughly covered in this 1997 book, with an emphasis on practical implementation. Computer code is available on the supporting website.

This book provides an accessible introduction to measure theory and stochastic calculus, and develops into an excellent users' guide to filtering. A complete resource for engineers, or anyone with an interest in implementation of filtering techniques. Three chapters concentrate on applications from finance, genetics and population modelling. Also includes exercises.

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an arterial or hierarchical net. Its determination requires a continuum formulation, which can however be simplified once a discrete structure begins to emerge. Connections are made with the masterly work of Bendsoe and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the World Wide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

This mathematically rigorous, practical introduction to the field of asymptotic statistics develops most of the usual topics of an asymptotics course, and also presents recent research topics such as empirical processes, the bootstrap, and semiparametric models.

Aimed at advanced undergraduate and graduate students in mathematics and related disciplines, this book presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches, with particular emphasis on the contrasts between them. Computational ideas are explained, as well as basic mathematical theory. Written in a lucid and informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on developments in statistical theory, including: material on Bayesian computation, such as MCMC, higher-order likelihood theory, predictive inference, bootstrap methods and conditional inference. It contains numerous extended examples of the application of formal inference techniques to real data, as well as historical commentary on the development of the subject. Throughout, the text concentrates on concepts, rather than mathematical detail, while maintaining appropriate levels of formality. Each chapter ends with a set of accessible problems.

Many electronic and acoustic signals can be modelled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterise the periodicity or near-periodicity of a signal and consequently to identify its source. This book presents and analyses several practical techniques used for such estimation. The problem of tracking slow frequency changes over time of a very noisy sinusoid is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large. Each chapter begins with a detailed overview, and many applications are given. Matlab code for the estimation techniques is also included. The book will thus serve as an excellent introduction and reference for researchers analysing such signals.

This user-friendly 2003 book explains the techniques and benefits of semiparametric regression in a concise and modular fashion.

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

This introduction to wavelet analysis and wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. The book contains numerous exercises and a website offering access to the time series and wavelet software.

This book introduces basic and advanced concepts of categorical regression with a focus on the structuring constituents of regression and recent developments in flexible and high-dimensional regression. Among the topics treated are nonparametric regression; the hurdle model and zero-inflated regression models for count data; and non-standard tree-based ensemble methods.

Describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students as well as statistical and interdisciplinary researchers. It is unusual in presenting Bayesian statistics with an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data.

The coordinate-free, or geometric, approach to the theory of linear models is more insightful, more elegant, more direct, and simpler than the more common matrix approach. This book treats Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting.

Choosing a model is central to all statistical work with data; this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. Real-data examples and exercises build familiarity with the methods.

This book explains in simple language how saddlepoint approximations make computations of probabilities tractible for complex models. No previous background in the area is required as the book introduces the subject from the very beginning. Many real data examples show the methods at work. For statisticians, biostatisticians, electrical engineers, econometricians, and applied mathematicians.

A self-contained graduate-level introduction to the statistical mechanics of disordered systems. In three parts, the book treats basic statistical mechanics; disordered lattice spin systems; and latest developments in the mathematical understanding of mean-field spin glass models. It assumes basic knowledge of classical physics and working knowledge of graduate-level probability theory.