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Most COVID-19 studies commonly report figures of the overall infection at a state- or county-level. This aggregation tends to miss out on fine details of virus propagation. In this paper, we analyze a high-resolution COVID-19 dataset in Cali, Colombia, that records the precise time and location of every confirmed case. We develop a non-stationary spatio-temporal point process equipped with a neural network-based kernel to capture the heterogeneous correlations among COVID-19 cases. The kernel is carefully crafted to enhance expressiveness while maintaining model interpretability. We also incorporate some exogenous influences imposed by city landmarks. Our approach outperforms the state-of-the-art in forecasting new COVID-19 cases with the capability to offer vital insights into the spatio-temporal interaction between individuals concerning the disease spread in a metropolis.

While random permutations of point processes are useful for generating counterfactuals in bivariate interaction tests, such permutations require that the underlying intensity be separable. In many real‐world datasets where clustering or inhibition is present, such an assumption does not hold. Here, we introduce a simple combinatorial optimization algorithm that generates second‐order preserving (SOP) point process permutations, for example, permutations of the times of events such that the function of the permuted process matches the function of the data. We apply the algorithm to synthetic data generated by a self‐exciting Hawkes process and a self‐avoiding point process, along with data from Los Angeles on earthquakes and arsons and data from Indianapolis on law enforcement drug seizures and overdoses. In all cases, we are able to generate a diverse sample of permuted point processes where the distribution of the functions closely matches that of the data. We then show how SOP point process permutations can be used in two applications: (1) bivariate Knox tests and (2) data augmentation to improve deep learning‐based space‐time forecasts.

Multivariate log-Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far been applied in bivariate cases only. We move beyond the bivariate case to model multispecies point patterns of tree locations. In particular we address the problems of identifying parsimonious models and of extracting biologically relevant information from the models fitted. The latent multivariate Gaussian field is decomposed into components given in terms of random fields common to all species and components which are species specific. This allows a decomposition of variance that can be used to quantify to what extent the spatial variation of a species is governed by common or species-specific factors. Cross-validation is used to select the number of common latent fields to obtain a suitable trade-off between parsimony and fit of the data. The selected number of common latent fields provides an index of complexity of the multivariate covariance structure. Hierarchical clustering is used to identify groups of species with similar patterns of dependence on the common latent fields.

We introduce a new multivariate product-shot-noise Cox process which is useful for modeling multi-species spatial point patterns with clustering intra-specific interactions and neutral, negative, or positive inter-specific interactions. The auto- and cross-pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward. We use the proposed process to model interactions within and among five tree species in the Barro Colorado Island plot.