ﻻ يوجد ملخص باللغة العربية
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we exploit the sparsity structure typical of (spatially) discretised log-Gaussian Cox process models by using approximate message-passing algorithms. The proposed algorithms scale well with the state dimension and the length of the temporal horizon with moderate loss in distributional accuracy. They hence provide a flexible and faster alternative to both non-linear filtering-smoothing type algorithms and to approaches that implement the Laplace method or expectation propagation on (block) sparse latent Gaussian models. We infer the parameters of the latent Gaussian model using a structured variational Bayes approach. We demonstrate the proposed framework on simulation studies with both Gaussian and point-process observations and use it to reconstruct the conflict intensity and dynamics in Afghanistan from the WikiLeaks Afghan War Diary.
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called textit{
Integro-difference equation (IDE) models describe the conditional dependence between the spatial process at a future time point and the process at the present time point through an integral operator. Nonlinearity or temporal dependence in the dynamic
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes proce
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form param
Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using thes