Robust algorithms for simulating spatial cluster processes

We review existing algorithms for generating simulated realisations of a spatial Neyman-Scott cluster point process and propose new algorithms. In real applications, the values of the model parameters passed to the algorithm can be extremely large or extremely small. The existing algorithms fail for such extreme cases, due to excessive computation time and memory demands. Fundamental reasons for this failure are analysed. We propose new algorithms that combine the best features of the existing algorithms and achieve control over the computation time and memory demands, even for extreme values of the model parameters. We analyse performance using theory and simulation experiments. Efficiency improvements of several orders of magnitude are achieved.