具有规则性和随机聚集性的空间点过程模型的近似贝叶斯推断
Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation
摘要：
本文提出了一个同时具有聚集性和排斥性的双随机空间点过程模型。该模型结合了施特劳斯过程和对数高斯考克斯过程背后的思想。该模型的可能性不能以封闭形式表达，但很容易在该模型下模拟实现。因此，我们解释了如何使用近似贝叶斯计算（ABC）进行统计推断这个模型。我们提出了一种基于后验预测和全局包络的模型验证方法。我们使用模拟点模式和真实数据示例来说明ABC程序和模型验证方法。
英文摘要：
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realisations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.
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