Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes
Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes
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DOI：
10.1111/rssb.12237
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发表时间：
2018-01-01
影响因子：
5.8
通讯作者：
Gamerman, Dani
中科院分区：
文献类型：
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作者：
Goncalves, Flavio B.;Gamerman, Dani
我们提出了一种新颖的推理方法来对时空 Cox 过程进行贝叶斯推理，其中强度函数取决于多元高斯过程。引入动态高斯过程以实现强度函数在离散时间上的演化。该方法的新颖之处在于，尽管似然函数的不可处理性和问题的无限维数，但不涉及离散化误差。该方法基于马尔可夫链蒙特卡罗算法，该算法从模型参数和潜在变量的联合后验分布中进行采样。事实证明，获得似然函数的主要测度的特定选择对于设计有效的马尔可夫链蒙特卡罗算法至关重要。这些模型以通用且灵活的方式定义，但由于对其组件进行了仔细的表征，因此它们适合从相关分布中直接采样。该模型还能够包含回归协变量和/或时间分量来解释强度函数的变异性。这些组件可能会受到与空间和/或时间的相关相互作用。真实和模拟的例子说明了方法，然后是结束语。
We present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to enable evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretization error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. A particular choice of the dominating measure to obtain the likelihood function is shown to be crucial to devise a valid Markov chain Monte Carlo algorithm. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions because of careful characterization of its components. The models also enable the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.