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 (RSPP), but their algorithm was not correctly detailed. In this paper, we correct their method and, based on this, we propose a new ABC-MCMC algorithm to which Markov property is introduced compared to a typical ABC method. Though it is generally impractical to use, Monte Carlo approximations can be leveraged for intractable terms. Another aspect of this paper is to explore the use of the exchange algorithm and the noisy Metropolis-Hastings algorithm (Alquier et al., 2016) on RSPP. Comparisons to ABC-MCMC methods are also provided. We find that the inferential approaches outlined above yield good performance for RSPP in both simulated and real data applications and should be considered as viable approaches for the analysis of these models.

翻译：针对似然函数难以处理的点过程模型，开发贝叶斯推断算法的研究日益受到关注。本文旨在阐述基于模拟的策略（包括近似贝叶斯计算（ABC）和马尔可夫链蒙特卡罗（MCMC）方法）在此类任务中的实用性。Shirota和Gelfand（2017）曾针对排斥性空间点过程（RSPP）提出扩展版ABC方法，但其算法描述存在缺陷。本文修正了原方法，并在此基础上提出一种新型ABC-MCMC算法——相较于传统ABC方法，该算法引入了马尔可夫性。尽管通常难以直接应用，蒙特卡洛近似可有效处理模型中的不可计算项。本文另一研究重点是在RSPP中探索交换算法与噪声Metropolis-Hastings算法（Alquier等人，2016）的应用，并与ABC-MCMC方法进行对比分析。研究发现，上述推断方法在模拟数据与真实数据应用中均对RSPP展现出良好性能，可作为分析此类模型的有效工具。