A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an autoregressive representation and the Laplace functional. Moreover, these results are used to derive the moment, predictive, and pair correlation measures of the proposed shot noise Cox process. The model is flexible but still tractable and allows for capturing persistence, global trends, and latent spatial and temporal factors. A Bayesian inference approach is adopted, and an efficient Markov Chain Monte Carlo procedure based on conditional Sequential Monte Carlo is proposed. An application to georeferenced wildfire data illustrates the properties of the model and inference.

翻译：本文提出了一种适用于时空数据的新型离散时间冲击噪声Cox过程。该过程的随机强度由一组具有依赖关系的潜伽马随机测度序列驱动。推导了潜过程的若干性质，包括自回归表示及拉普拉斯泛函。此外，利用这些结果导出了所提冲击噪声Cox过程的矩、预测及配对相关测度。该模型兼具灵活性与可解性，能够捕获持续性、全局趋势以及潜在时空因子。采用贝叶斯推断方法，并基于条件序贯蒙特卡洛提出一种高效马尔可夫链蒙特卡洛算法。对地理参考野火数据的应用分析验证了模型及其推断方法的特性。