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Keywords:

  • empirical Bayesian inference;
  • ergodicity;
  • Markov chain Monte Carlo;
  • Metropolis-adjusted Langevin algorithm;
  • multivariate Cox processes;
  • Neyman–Scott processes;
  • pair correlation function;
  • parameter estimation;
  • spatial point processes;
  • third-order properties

Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and third-order properties are studied and utilized in the statistical analysis of clustered point patterns. Also empirical Bayesian inference for the underlying intensity surface is considered.