Journal ArticleDOI
Log Gaussian Cox Processes
TLDR
Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases and the appealing properties of such models are demonstrated theoretically as well as through data examples and simulations.Abstract:
Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and third-order properties are studied and utilized in the statistical analysis of clustered point patterns. Also empirical Bayesian inference for the underlying intensity surface is considered.read more
Citations
More filters
Journal ArticleDOI
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
TL;DR: This work considers approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non‐Gaussian response variables and can directly compute very accurate approximations to the posterior marginals.
Book
Model-based Geostatistics
TL;DR: An overview of model-based geostatistics can be found in this paper, where a generalized linear model is proposed for estimating geometrical properties of geometrically constrained data.
Journal ArticleDOI
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
TL;DR: It is shown that, using an approximate stochastic weak solution to (linear) stochastically partial differential equations, some Gaussian fields in the Matérn class can provide an explicit link, for any triangulation of , between GFs and GMRFs, formulated as a basis function representation.
Book
Applied Spatial Statistics for Public Health Data
Lance A. Waller,Carol A. Gotway +1 more
TL;DR: In this paper, the authors present a method for estimating risk and risk of cancer in public health data using statistical methods for spatial data in the context of geographic information systems (GISs).
Journal ArticleDOI
General state space Markov chains and MCMC algorithms
TL;DR: In this paper, a survey of results about Markov chains on non-countable state spaces is presented, along with necessary and sufficient conditions for geometrical and uniform ergodicity along with quantitative bounds on the rate of convergence to stationarity.
References
More filters
Book
Statistics for spatial data
Noel A Cressie,Noel A Cressie +1 more
TL;DR: In this paper, the authors present a survey of statistics for spatial data in the field of geostatistics, including spatial point patterns and point patterns modeling objects, using Lattice Data and spatial models on lattices.
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.