Spatial Capture–Recapture Models

Properties of Spatial Cox Process Models

Probabilistic properties of Cox processes of relevance for statistical modeling and inference are studied. Particularly, we study the most important classes of Cox processes, including log Gaussian Cox processes, shot noise Cox processes, and permanent Cox processes. We consider moment properties and point process operations such as thinning, displacements, and superpositioning. We also discuss...

Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Spatial Nonparametric Bayesian Models

The prior distribution is an essential ingredient of any Bayesian analysis, and it plays a major role in determining the final results. As such, Bayesians attempt to use prior distributions that have certain properties. Perhaps the main property is a desire to accurately reflect prior information, i.e., information external to the experiment at hand. We would supplement this vague property with...

Multivariate Spatial Process Models

Stochastic Spatial Models

In the models we will consider, space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites. Our main aim here is to explain an idea of Durrett and Levin (1994): the behavior of these models can be predicted from the properties of the mean field ODE, i.e., the equations for the densities o...