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一般度量图上的对数高斯 Cox 过程AI 解读

Abstract The modelling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging Gaussian Whittle–Matérn fields, which are solutions to fractional-order stochastic differential equations on metric graphs. To achieve computationally efficient likelihood-based inference,…

度量图上高斯 Whittle–Matérn 随机场的统计推断AI 解读

Abstract Whittle–Matérn fields are a recently introduced class of Gaussian processes on metric graphs, specified as solutions to a fractional-order stochastic differential equation. Unlike previous covariance-based methods, these fields are well-defined for any compact metric graph and can provide Gaussian processes with differentiable sample paths. We derive the main statistical properties, including the consistency and asymptotic normality of maximum likelihood estimators…