# The SPP Procedure

#### Likelihood Methods for Model Fitting

The intensity function is assumed to be log linear in the parameters . So

where is a real-valued or vector-valued function of location s. can include a polynomial function of coordinate variables or a spatial covariate. The log likelihood for the parameters is given by

The integral in the expression for the log likelihood can be approximated using quadrature as

for some quadrature weights . Hence, the log likelihood can be rewritten as follows:

Based on the observation by Berman and Turner (1992) and Baddeley and Turner (2000), the log likelihood can be approximated as

where . If the list of points also includes the collection of data points , then and

The log pseudolikelihood can be maximized using standard optimization algorithms.