# Posts tagged spatial

## Modeling spatial point patterns with a marked log-Gaussian Cox process

The log-Gaussian Cox process (LGCP) is a probabilistic model of point patterns typically observed in space or time. It has two main components. First, an underlying intensity field $$\lambda(s)$$ of positive real values is modeled over the entire domain $$X$$ using an exponentially-transformed Gaussian process which constrains $$\lambda$$ to be positive. Then, this intensity field is used to parameterize a Poisson point process which represents a stochastic mechanism for placing points in space. Some phenomena amenable to this representation include the incidence of cancer cases across a county, or the spatiotemporal locations of crime events in a city. Both spatial and temporal dimensions can be handled equivalently within this framework, though this tutorial only addresses data in two spatial dimensions.