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Keywords:

  • Bayesian inference;
  • conditional intensity;
  • Cox process;
  • Gibbs point process;
  • Markov chain Monte Carlo;
  • maximum likelihood;
  • perfect simulation;
  • Poisson process;
  • residuals;
  • simulation free estimation;
  • summary statistics

Abstract.  We summarize and discuss the current state of spatial point process theory and directions for future research, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications. In particular, we consider Poisson, Gibbs and Cox process models, diagnostic tools and model checking, Markov chain Monte Carlo algorithms, computational methods for likelihood-based inference, and quick non-likelihood approaches to inference.