Likelihood based inference for log Gaussian Cox processes

Log Gaussian Cox processes are a flexible class of doubly stochastic point processes obtained by conditioning on a Gaussian random field Y and considering a Poisson point process with intensity log(Y). The restriction of this point process to a bounded region R has a density f with respect to the unit rate Poisson process: for any finite point configuration x contained in R and of cardinality n, f(x) is given by the product of the density at x of the n’th order reduced moment measure of the process times a void probability for another log Gaussian Cox process where the underlying Gaussian random field has the same covariance function as Y but a mean function depending on x. This result is exploited for likelihood based inference.