Statistical inference for highly multivariate point pattern data is challenging due to complex models with large numbers of parameters. In this paper we develop numerically stable and efficient parameter estimation and model selection algorithms for a class of multivariate log Gaussian Cox processes. The methodology is applied to a highly multivariate point pattern data set from tropical rain forest ecology.

Keywords: cross pair correlation, elastic net, LASSO, log Gaussian Cox process, multivariate point process, proximal Newton method.