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.

翻译：随着对具有不可处理似然函数的点过程模型开发贝叶斯推断算法的需求日益增加，本文旨在阐述基于模拟策略（包括近似贝叶斯计算和马尔可夫链蒙特卡洛方法）在该任务中的实用性。Shirota与Gelfand（2017）针对排斥性空间点过程（如Strauss点过程和行列式点过程）提出了一种扩展版ABC方法，但其算法细节存在错误。我们指出该算法在一般情况下难以处理且实际应用受限（除少数约束场景外），因此促使我们转而考虑Fearnhead与Prangle（2012）提出的ABC-MCMC算法。进一步地，我们探索了交换算法与近期提出的带噪Metropolis-Hastings算法（Alquier等，2016）的联合应用。作为交换算法的扩展（该算法每次迭代需从似然函数中生成单次模拟），带噪Metropolis-Hastings算法从同一似然函数中获取多次抽样。经模拟数据与实际数据验证，这两种推断方法对排斥性空间点过程均表现出良好性能，应被视为分析此类模型的有效方案。