Palm distributions for log Gaussian Cox processes

叠加点过程的Palm分布用于统计推断

Palm distributions of superposed point processes for statistical inference

本文研究了叠加点过程的Palm分布，提出了最小对比估计和射线噪声Cox过程的高阶Palm分布推导方法，为统计推断提供了新的工具。

Log Gaussian Cox processes on the sphere

A log Gaussian Cox process (LGCP) is a doubly stochastic construction consisting of a Poisson point process with a random log-intensity given by a Gaussian random field. Statistical methodology have mainly been developed for LGCPs defined in the $d$-dimensional Euclidean space. This paper concerns the case of LGCPs on the $d$-dimensional sphere, with $d=2$ of primary interest. We discuss the existence problem of such LGCPs, provide sufficient existence conditions, and establish further useful theoretical properties. The results are applied for the description of sky positions of galaxies, in c…

Going off grid: Computationally efficient inference for log-Gaussian Cox processes

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, while an approximation based on a counting process on a partition of the domain only achieves first-order convergence. The given results improve on the general theory of convergence of the stochastic partial differential equation models, introd…

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this art…

Asymptotics for minimisers of convex processes

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to a fair range of different statistical estimation problems, including Cox regression, logistic and Poisson regression, least absolute deviation regression outside model conditions, and pseudo-likelihood estimation for Markov chains. Our paper has two aims. The first is to exposit the method itself, which in many cases, under reasonable regularity conditions,…

线性网络上由变换高斯过程驱动的Cox过程——综述与新贡献

Cox processes driven by transformed Gaussian processes on linear networks -- A review and new contributions

本文针对线性网络上点过程模型缺乏的问题，提出由变换高斯过程驱动的三类Cox过程模型，并首次给出参数族统计推断方法、模拟算法及度量选择的讨论。