Books in the Cambridge Series in Statistical and Probabilistic Mathematics series

Network science is one of the fastest growing areas in science and business. This classroom-tested, self-contained book is designed for master's-level courses and provides a rigorous treatment of random graph models for networks, featuring many examples of real-world networks for motivation and numerous exercises to build intuition and experience.

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics and researchers who use statistical methods. Backgrounds in calculus and linear algebra are important, and a course in elementary mathematical analysis useful, but not required. An appendix summarizes the mathematical definitions and results outlined.

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.

A textbook for students with some background in probability that develops quickly a rigorous theory of Markov chains and shows how actually to apply it, e.g. to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice.

This 2004 introduction to ways of modelling phenomena that occur over time is accessible to anyone with a basic knowledge of statistical ideas. Examples from physical, biological and social sciences show how the principles can be put into practice: data sets and R code for these are supplied on author's website.

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.

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.