04 Cross Validation for Log Gaussian Cox process

Oregon Convention Center 

The Log Gaussian Cox process(LGCP) is arguably one of the most used model based strategy to analyze spatial point pattern(SPP) data. In practice, we usually have different models with increasing levels of complexity that we need to criticize, assess our assumptions and validate. This work is an attempt to provide a practical solution, under a Bayesian framework, to some of these problems using Cross Validation(CV). The challenge is that, contrary to traditional CV approach based on the expected log point-wise predictive density, in SPP analysis there is no concept of data-point to be removed, which then requires a group-wise or region-wise definition for the log predictive density. For this purpose, we propose a natural extension of the expected log predictive, better suited for LGCP, that could be termed expected log region-wise or group-wise predictive density. We also provide a very accurate, fast and deterministic approximation obtained from a single run of the model that we validate with Monte Carlo samples. We expect to make the solution available in the R-INLA software.

Log gaussian cox process

cross validation

INLA

model selection 

Section on Bayesian Statistical Science