This paper proposes a novel family of geostatistical models to account for features that cannot be properly accommodated by traditional Gaussian processes. The family is specified hierarchically and combines the infinite-dimensional dynamics of Gaussian processes with that of any multivariate continuous distribution. This combination is stochastically defined through a latent Poisson process and the new family is called the Poisson-Gaussian Mixture Process - POGAMP. Whilst the attempt of defining geostatistical processes by assigning some arbitrary continuous distribution to be the finite-dimension distributions usually leads to non-valid processes, the finite-dimensional distributions of the POGAMP can be arbitrarily close to any continuous distribution and still define a valid process. Formal results to establish the existence and some important properties of the POGAMP, such as absolute continuity with respect to a Gaussian process measure, are provided. Also, an MCMC algorithm is carefully devised to perform Bayesian inference when the POGAMP is discretely observed in some space domain.
翻译:本文建议建立一个新型的地理统计模型体系,以说明传统高斯进程无法适当容纳的特征。 家庭按等级划分,并将高斯进程的无限维度动态与任何多变量连续分布的动态结合起来。 这种组合通过潜伏的 Poisson 进程进行随机界定,而新的家庭称为Pooisson-Gausian Mixture进程 - POGAMP。 尽管试图通过将某些任意连续分布指定为有限二元分布通常导致非有效过程来界定地理统计进程,但POGAMP的有限维度分布可以任意接近任何连续分布,并且仍然界定一个有效的过程。 提供了确定POGAMP的存在和某些重要特性的正式结果,例如与高斯进程测量尺度有关的绝对连续性。 另外,当POGAMP在某些空间领域被独立观测时,还仔细设计了一种MC算法来进行Bayesian的推断。