Spatio-temporal point process data arise in many fields of application. An intuitively natural way to specify a model for a spatio-temporal point process is through its conditional intensity at location x and time t, given the history of the process up to time t. Typically, this results in an analytically intractable likelihood. Likelihood-based inference therefore relies on Monte Carlo methods which are computationally intensive and require careful tuning to each application. We propose a partial likelihood alternative which is computationally straightforward and can be applied routinely. We apply the method to data from the 2001 foot-and-mouth epidemic in the UK, using a previously published model for the spatio-temporal spread of the disease.
Diggle, Peter J., "A Partial Likelihood for Spatio-temporal Point Processes" (June 2005). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 75.