Fitting Log-Gaussian Cox Processes Using Generalized Additive Model Software

While log-Gaussian Cox process regression models are useful tools for modeling point patterns, they can be technically difficult to fit and require users to learn/adopt bespoke software. We show that, for suitably formatted data, we can actually fit these models using generalized additive model software, via a simple line of code, demonstrated on R by the popular mgcv package. We are able to do this because a common and computationally efficient way to fit a log-Gaussian Cox process model is to use a basis function expansion to approximate the Gaussian random field, as is provided by a generic bivariate smoother over geographic space. We further show that if basis functions are parameterized appropriately then we can estimate parameters in the spatial covariance function for the latent random field using a generalized additive model. We use simulation to show that this approach leads to model fits of comparable quality to state-of-the-art software, often more quickly. But we see the main advance from this work as lowering the technology barrier to spatial statistics for applied researchers, many of whom are already familiar with generalized additive model software.尽管对数高斯柯克斯过程回归模型 (log-Gaussian Cox Process Regression Model) 是点模式 (Point Pattern) 建模的有效工具，但其拟合在技术层面存在难度，且要求使用者学习或采用定制软件。本研究表明，对于格式规范的数据集，我们可借助广义加性模型 (Generalized Additive Model, GAM) 软件完成此类模型的拟合，仅需一行简单代码；该方法通过广受欢迎的mgcv包 (mgcv package) 在R语言中得以演示。本方法可行的原因在于，拟合对数高斯柯克斯过程模型的通用且计算高效的路径，是利用基函数展开 (Basis Function Expansion) 近似高斯随机场 (Gaussian Random Field)，而地理空间上的通用双变量平滑器 (Bivariate Smoother) 即可提供此类展开。本研究进一步证明，若基函数的参数设置合理，即可通过广义加性模型估计潜在随机场 (Latent Random Field) 的空间协方差函数 (Spatial Covariance Function) 中的参数。我们通过模拟实验 (Simulation) 证明，该方法得到的模型拟合效果可与当前顶尖软件媲美，且通常运算速度更快。但本研究的核心贡献在于，降低了应用研究者接触空间统计学 (Spatial Statistics) 的技术门槛——这类研究者中多数已熟悉广义加性模型软件。