Spatial statistics is concerned with the analysis of data that have spatial locations associated them, and those are used to model statistical dependence between data. The treated as a single realization from probability encodes through both fixed effects random effects, where randomness manifest in underlying process noisy, incomplete measurement process. focus this review article on use basis...

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...

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...

Discrete spatial heterogenity is introduced into disease transmission models, resulting in large systems of ordinary differential equations. Such metapopulation models describe disease spread on a number of spatial patches. In the first model considered, there is no explicit movement of individuals; rather infectives can pass the disease to susceptibles in other patches. The second type of mode...

There are many simple, everyday tasks, such as following road directions, using instructions to assemble a bicycle, reading a novel, or helping to solve your child’s geometry homework, that seem to entail constructing a spatial mental model from a description. In order to comprehend Go straight till the jrs t light, then turn left, go down about three blocks to Oak, and make a right, it is usef...

the significance of spatial heterogeneity in understanding ecological processes has been recognized long ago. one of the earliest expressions of this recognition is the habitat heterogeneity hypothesis that links spatial  heterogeneity to niche vegetation patterns formation and species coexistence. yet, an  important if not crucial  aspect of landscape heterogeneity has escaped deep considerati...

Spatial statistical models have been used extensively in many geospatial and environmental studies over several decades. While being very important, the issues of testing and validation in spatial statistical models are rarely investigated carefully in spatial environmental studies. Often strict theoretical asymptotic assumptions used in those models are left unexplored or unanswered in many st...

Although a large literature on delegation exists, few models have pushed beyond a core set of canonical assumptions. This approach may be justified on grounds of tractability, but the failure to grasp the significance of different assumptions and push beyond specific models has limited our understanding of the incentives for delegation. Consequently, the justifications for delegation that have ...

Which model and which spatial analysis? The spatial dimension plays a key role in many social phenomena. On the one hand things are unequally distributed through space, creating spatial differentiation, segregation, discontinuities. On the other hand there is a feedback loop between a society's organization and a space's configuration. Most of the time, the modeling of spatial phenomena and pro...