AI 中文总结
针对非齐次二元对数高斯考克斯过程，提出两步模拟估计法，结合经典泊松估计与神经网络模拟推理，分离估计降低复杂度，引入二维图像输入，模拟结果显示能准确估计潜场参数，且具实际适用性。
AI 中文摘要
我们提出了一种计算高效的基于模拟的估计方法，用于非齐次二元对数高斯考克斯过程，采用两步程序。它将一阶参数的经典泊松估计与基于神经网络的潜场参数模拟推理相结合。通过分离估计，降低了高维参数估计的复杂性，减少了在有协变量时基于模拟方法指定宽泛参数范围的需求。此外，引入二维图像输入使模型能直接学习空间信息。模拟结果表明该方法能准确估计潜场参数，并用大猩猩数据集说明了其实际适用性。
英文摘要
We propose a computationally efficient simulation-based estimation method with a two-step procedure for inhomogeneous bivariate Log-Gaussian Cox Processes. It combines classical Poisson estimation for the first-order parameters with simulation-based inference using neural networks for the latent field parameters. By separating the estimations, it reduces the complexity of high dimensional parameter estimation and the need for the simulation-based method to specify broad parameter ranges in the presence of covariates. In addition, we introduce two dimensional image inputs that enable the model to learn spatial information directly. Simulation results demonstrate that the proposed approach provides accurate estimates of the latent field parameters. We further illustrate the method's practical applicability using the gorilla dataset.
