Journal ArticleDOI
Generalized gamma measures and shot-noise Cox processes
TLDR
In this paper, a parametric family of completely random measures, which includes gamma random measures and positive stable random measures as well as inverse Gaussian measures, is defined and used in a shot-noise construction as intensity measures for Cox processes.Abstract:
A parametric family of completely random measures, which includes gamma random measures, positive stable random measures as well as inverse Gaussian measures, is defined. In order to develop models for clustered point patterns with dependencies between points, the family is used in a shot-noise construction as intensity measures for Cox processes. The resulting Cox processes are of Poisson cluster process type and include Poisson processes and ordinary Neyman-Scott processes. We show characteristics of the completely random measures, illustrated by simulations, and derive moment and mixing properties for the shot-noise random measures. Finally statistical inference for shot-noise Cox processes is considered and some results on nearest-neighbour Markov properties are given.read more
Citations
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Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Journal ArticleDOI
Modern Statistics for Spatial Point Processes
TL;DR: In this article, the current state of spatial point process theory and directions for future research are summarized and discussed, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications.
Book ChapterDOI
Models beyond the Dirichlet process
Antonio Lijoi,Igor Prünster +1 more
TL;DR: In this paper, the authors provide a review of Bayesian nonparametric models that go beyond the Dirichlet process, and show that in some cases of interest for statistical applications, the DPM is not an adequate prior choice.
Journal ArticleDOI
Controlling the reinforcement in Bayesian non-parametric mixture models
TL;DR: A Bayesian non‐parametric approach is taken and adopt a hierarchical model with a suitable non-parametric prior obtained from a generalized gamma process to solve the problem of determining the number of components in a mixture model.
Journal ArticleDOI
Sparse graphs using exchangeable random measures
François Caron,Emily B. Fox +1 more
TL;DR: In this paper, completely random measures (CRMs) are used to define the exchangeable random measure (CRM) to achieve sparse graphs while maintaining the attractive properties of exchangeability.
References
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Book
Stochastic Geometry and Its Applications
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
BookDOI
An introduction to the theory of point processes
Daryl J. Daley,David Vere-Jones +1 more
TL;DR: An introduction to the theory of point processes can be found in this article, where the authors introduce the concept of point process and point process theory and introduce point processes as a theory for point processes.
Book
Statistical analysis of spatial point patterns
TL;DR: This book provides an introduction to statistical methods for analysing data in the form of spatial point distributions, described in intuitive terms and illustrated by many applications to real data drawn from the biological and biomedical sciences.
Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Book
Stochastic Simulation
TL;DR: Brian D. Ripley's Stochastic Simulation is a short, yet ambitious, survey of modern simulation techniques, and three themes run throughout the book.
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