Log-Gaussian Cox processes (LGCPs) are a popular and flexible tool for modelling point pattern data. While maximum likelihood estimation of the parameters of such a model is attractive in principle, the likelihood function is not available in closed form. Various Monte Carlo approximations have been proposed, but these have seen very limited use in the literature and are often dismissed as impractical. This article provides a comprehensive study of the computational properties of Monte Carlo maximum likelihood estimation (MCMLE) for LGCPs. We compare various importance sampling algorithms for MCMLE, and also consider their performance against other methods of inference (such as minimum contrast) in numerical studies. We find that the best MCMLE algorithm is a practical proposition for parameter estimation given modern computing power, but the performance of this methodology is rather sensitive to the choice of reference parameters defining the importance sampling distribution.

对数高斯 Cox 过程 (LGCP) 是一种流行且灵活的点模式数据建模工具。虽然这种模型的参数的最大似然估计原则上很有吸引力，但似然函数在封闭形式中不可用。人们已经提出了各种蒙特卡洛近似，但这些近似在文献中的使用非常有限，并且经常被认为不切实际而被忽视。本文对 LGCP 的蒙特卡罗最大似然估计 (MCMLE) 的计算特性进行了全面研究。我们比较了 MCMLE 的各种重要性采样算法，并考虑了它们与其他推理方法（例如最小对比度）的性能数值研究。我们发现，考虑到现代计算能力，最佳 MCMLE 算法是参数估计的实用命题，但该方法的性能对定义重要性采样分布的参考参数的选择相当敏感。