  There is increasing interest to develop Bayesian inferential algorithms for
point process models with intractable likelihoods. A purpose of this paper is
to illustrate the utility of using simulation based strategies, including
approximate Bayesian computation (ABC) and Markov chain Monte Carlo (MCMC)
methods for this task. Shirota and Gelfand (2017) proposed an extended version
of an ABC approach for repulsive spatial point processes, including the Strauss
point process and the determinantal point process, but their algorithm was not
correctly detailed. We explain that is, in general, intractable and therefore
impractical to use, except in some restrictive situations. This motivates us to
instead consider an ABC-MCMC algorithm developed by Fearnhead and Prangle
(2012). We further explore the use of the exchange algorithm, together with the
recently proposed noisy Metropolis-Hastings algorithm (Alquier et al., 2016).
As an extension of the exchange algorithm, which requires a single simulation
from the likelihood at each iteration, the noisy Metropolis-Hastings algorithm
considers multiple draws from the same likelihood function. We find that both
of these inferential approaches yield good performance for repulsive spatial
point processes in both simulated and real data applications and should be
considered as viable approaches for the analysis of these models.
