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.

Spatial point processes play a fundamental role in spatial statistics and today they are a very active area of research with many new and emerging applications. Although published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and nowhere can one find a comprehensive treatment of the theory and applications of simulation-based inference. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo (MCMC) algorithms and explore one of the most important recent developments in MCMC-perfect simulation procedures.

The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.

Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time covariance functions. The contributors then describe stochastic and statistical models that are used to generate simulated rainfall sequences for hydrological use, such as flood risk assessment. The final chapter explores Gaussian Markov random field specifications and Bayesian computational inference via Gibbs sampling and Markov chain Monte Carlo, illustrating the methods with a variety of data examples, such as temperature surfaces, dioxin concentrations, ozone concentrations, and a well-established deterministic dynamical weather model.

Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians is the lack of a suitable text introducing the modern co-ordinate free approach to differential geometry in a manner accessible to statisticians.

Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time covariance functions. The contributors then describe stochastic and statistical models that are used to generate simulated rainfall sequences for hydrological use, such as flood risk assessment. The final chapter explores Gaussian Markov random field specifications and Bayesian computational inference via Gibbs sampling and Markov chain Monte Carlo, illustrating the methods with a variety of data examples, such as temperature surfaces, dioxin concentrations, ozone concentrations, and a well-established deterministic dynamical weather model.

Infectious disease accounts for more death and disability worldwide than either noninfectious disease or injury. This book contains a number of different quantitative approaches to understanding the patterns of such diseases in populations, and the design of control strategies to lessen their effect. The papers are written by experts with varied mathematical expertise and involvement in biological, medical and social sciences. The volume increases interaction between specialties by describing research on many infectious diseases that affect humans, including viral diseases, such as measles and AIDS, and tropical parasitic infections. Sections deal with problems relating to transmissible diseases with long development times (such as AIDS); vaccination strategies; the consequences of treatment interventions; the dynamics of immunity; heterogeneity of populations; and prediction. On each topic, the editors have chosen papers that bring together contrasting approaches via the development of theoretical results, the use of relevant knowledge from applied fields, and the analysis of data.

The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood.

Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.

Infectious disease accounts for more death and disability worldwide than either noninfectious disease or injury. This book contains a number of different quantitative approaches to understanding the patterns of such diseases in populations, and the design of control strategies to lessen their effect. The papers are written by experts with varied mathematical expertise and involvement in biological, medical and social sciences. The volume increases interaction between specialties by describing research on many infectious diseases that affect humans, including viral diseases, such as measles and AIDS, and tropical parasitic infections. Sections deal with problems relating to transmissible diseases with long development times (such as AIDS); vaccination strategies; the consequences of treatment interventions; the dynamics of immunity; heterogeneity of populations; and prediction. On each topic, the editors have chosen papers that bring together contrasting approaches via the development of theoretical results, the use of relevant knowledge from applied fields, and the analysis of data.

Set-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved. Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.