Point Processes with a Generalized Order Statistic Property


Book Description

Mixed Poisson processes are a well known class of point processes derived from (stationary) Poisson processes. In particular they cover cases where the intensity of a Poisson process is unknown but can be assumed to follow a known probability distribution. This situation is common e. g. in insurance mathematics where for instance the number of accident claims in which an individual is involved and which is evolving over some time can in principal be well described by a Poisson process with an individual, yet normally unknown intensity corresponding to the individual's accident proneness. Modelling this intensity as a random variable naturally leads to a mixed model. Usually, an insurance company will have a good estimate of the associated mixing distribution due to its large portfolio of policies.




Handbook of Spatial Point-Pattern Analysis in Ecology


Book Description

Understand How to Analyze and Interpret Information in Ecological Point Patterns Although numerous statistical methods for analyzing spatial point patterns have been available for several decades, they haven’t been extensively applied in an ecological context. Addressing this gap, Handbook of Spatial Point-Pattern Analysis in Ecology shows how the techniques of point-pattern analysis are useful for tackling ecological problems. Within an ecological framework, the book guides readers through a variety of methods for different data types and aids in the interpretation of the results obtained by point-pattern analysis. Ideal for empirical ecologists who want to avoid advanced theoretical literature, the book covers statistical techniques for analyzing and interpreting the information contained in ecological patterns. It presents methods used to extract information hidden in spatial point-pattern data that may point to the underlying processes. The authors focus on point processes and null models that have proven their immediate utility for broad ecological applications, such as cluster processes. Along with the techniques, the handbook provides a comprehensive selection of real-world examples. Most of the examples are analyzed using Programita, a continuously updated software package based on the authors’ many years of teaching and collaborative research in ecological point-pattern analysis. Programita is tailored to meet the needs of real-world applications in ecology. The software and a manual are available online.




Handbook of Environmental and Ecological Statistics


Book Description

This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface. Features: An internationally regarded editorial team. A distinguished collection of contributors. A thoroughly contemporary treatment of a substantial interdisciplinary interface. Written to engage both statisticians as well as quantitative environmental researchers. 34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science.







Statistical Inference and Simulation for Spatial Point Processes


Book Description

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. 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 algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.




An Introduction to the Theory of Point Processes


Book Description

Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments.




Applied Probability


Book Description







Financial Signal Processing and Machine Learning


Book Description

The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches. Key features: Highlights signal processing and machine learning as key approaches to quantitative finance. Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems. Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques. Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.




An Introduction to the Theory of Point Processes


Book Description

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.