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We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.

In environmetrics, interest often centres around the development of models and methods for making inference on observed point patterns assumed to be generated by latent spatial or spatio-temporal processes, which may have a hierarchical structure. In this research, motivated by the analysis of spatio-temporal storm cell data, we generalize the Neyman–Scott parent–child process to account for hierarchical clustering. This is accomplished by allowing the parents to follow a log-Gaussian Cox process thereby incorporating correlation and facilitating inference at all levels of the hierarchy. This approach is applied to monthly storm cell data from the Bismarck, North Dakota radar station from April through August 2003 and we compare these results to simpler cluster processes to demonstrate the advantages of accounting for both levels of correlation present in these hierarchically clustered point patterns. En environnemétrie, il est courant de s’intéresser au développement de modèles et de méthodes d’inférence pour les motifs de points générés par des processus latents spatiaux ou spatio-temporels, lesquels peuvent provenir d’une structure hiérarchique. Motivés par l’analyse de données spatio-temporelles sur les cellules de tempêtes, les auteurs généralisent le processus parent-enfant de Neyman-Scott pour tenir compte de la structure hiérarchique en grappe. Le fait de laisser les parents suivre un processus de Cox log-gaussien permet d’incorporer de la corrélation et de faciliter l’inférence à tous les niveaux de la hiérarchie. Les auteurs utilisent cette approche avec les données mensuelles de cellules de tempête de la station de radar de Bismarck, dans le Dakota du Nord, pour la période d’avril à août 2003. Ils comparent ces résultats à ceux obtenus avec des processus en grappe plus simples et démontrent les avantages liées à un modèle qui tient compte de la corrélation aux deux niveaux pour de tels processus ponctuels hiérarchiques en grappe.

Spatio-temporal Cox point process models with a multiplicative structure for the driving random intensity, incorporating covariate information into temporal and spatial components, and with a residual term modelled by a shot-noise process, are considered. Such models are flexible and tractable for statistical analysis, using spatio-temporal versions of intensity and inhomogeneous K-functions, quick estimation procedures based on composite likelihoods and minimum contrast estimation, and easy simulation techniques. These advantages are demonstrated in connection with the analysis of a relatively large data set consisting of 2796 days and 5834 spatial locations of fires. The model is compared with a spatio-temporal log-Gaussian Cox point process model, and likelihood-based methods are discussed to some extent.

Landscape heterogeneity affects population dynamics, which determine species persistence, diversity and interactions. These relationships can be accurately represented by advanced spatially-explicit models (SEMs) allowing for high levels of detail and precision. However, such approaches are characterised by high computational complexity, high amount of data and memory requirements and spatio-temporal outputs may be difficult to analyse. A possibility to deal with this complexity is to aggregate outputs over time or space, but then interesting information may be masked and lost, such as local spatio-temporal relationships or patterns. An alternative solution is given by meta-models and meta-analysis, where simplified mathematical relationships are used to structure and summarise the complex transformations from inputs to outputs. Here, we propose an original approach to analyse SEM outputs. By developing a meta-modelling approach based on spatio-temporal point processes (STPPs), we characterise spatio-temporal population dynamics and landscape heterogeneity relationships in agricultural contexts. A landscape generator and a spatially-explicit population model simulate hierarchically the pest-predator dynamics of codling moth and ground beetles in apple orchards over heterogeneous agricultural landscapes. Spatio-temporally explicit outputs are simplified to marked point patterns of key events, such as local proliferation or introduction events. Then, we construct and estimate regression equations for multi-type STPPs composed of event occurrence intensity and magnitudes. Results provide local insights into spatio-temporal dynamics of pest-predator systems. We are able to differentiate the contributions of different driver categories (i.e. spatio-temporal, spatial, population dynamics). We highlight changes in the effects on occurrence intensity and magnitude when considering drivers at global or local scale. This approach leads to novel findings in agroecology where, for example, we show that the organisation of cultivated patches and semi-natural elements play different roles for pest regulation depending on the scale considered. It aids to formulate guidelines for biological control strategies at global and local scale.

Short-time human travel behaviour can be described by a power law with respect to distance. We incorporate this information in space–time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a spatio-temporal point process model for individual-level data and a multivariate time-series model for aggregated count data. In both frame-works, a power-law decay of spatial interaction is embedded into the epidemic component and estimated jointly with all other unknown parameters using (penalised) likelihood inference. Whereas the power law can be based on Euclidean distance in the point process model, a novel formulation is proposed for count data where the power law depends on the order of the neighbourhood of discrete spatial units. The performance of the new approach is investigated by a reanalysis of individual cases of invasive meningococcal disease in Germany (2002–2008) and count data on influenza in 140 administrative districts of Southern Germany (2001–2008). In both applications, the power law substantially improves model fit and predictions, and is reasonably close to alternative qualitative formulations, where distance and order of neighbourhood, respectively, are treated as a factor. Implementation in the R package surveillance allows the approach to be applied in other settings.

We proposed a method to extract causal relations of spatial clusters from multi-dimensional event sequence data, also known as a spatio-temporal point process. The proposed Granger cluster sequence mining algorithm identifies the pairs of spatial data clusters that have causality over time with each other. It extended the cluster sequence mining algorithm, which utilized a statistical inference technique to identify the occurrence relation, with a causality inference based on the Granger causality. In addition, the proposed method utilizes a false discovery rate procedure to control the significance of the causality. Based on experiments on both synthetic and semi-real data, we confirmed that the algorithm is able to extract the synthetic causal relations from multiple different sets of data, even when disturbed with high level of spatial noise. False discovery rate procedure also helps to increase the accuracy even more under such case and also make the algorithm less-sensitive to the hyperparameters.

Efforts to understand population dynamics and identify high-quality habitat require information about spatial variation in demographic parameters. However, estimating demographic parameters typically requires labor-intensive capture–recapture methods that are difficult to implement over large spatial extents. Spatially explicit integrated population models (IPMs) provide a solution by accommodating spatial capture–recapture (SCR) data collected at a small number of sites with survey data that may be collected over a much larger extent. We extended the spatial IPM framework to include a spatio-temporal point process model for recruitment, and we applied the model to 4 yr of SCR and distance-sampling data on Canada Warblers (Cardellina canadensis) near the southern extent of the species' breeding range in North Carolina, USA, where climate change is predicted to cause population declines and distributional shifts toward higher elevations. To characterize spatial variation in demographic parameters over the climate gradient in our study area, we modeled density, survival, and per capita recruitment as functions of elevation. We used a male-only model because males comprised >90% of our point-count detections. Apparent survival was low but increased with elevation, from 0.040 (95% credible interval [CI]: 0.0032–0.12) at 900 m to 0.29 (95% CI: 0.16–0.42) at 1,500 m. Recruitment was not strongly associated with elevation, yet density varied greatly, from <0.03 males ha–1 below 1,000 m to >0.2 males ha–1 above 1,400 m. Point estimates of population growth rate were <1 at all elevations, but 95% CIs included 1. Additional research is needed to assess the possibility of a long-term decline and to examine the effects of abiotic variables and biotic interactions on the demographic parameters influencing the species' distribution. The modeling framework developed here provides a platform for addressing these issues and advancing knowledge about spatial demography and population dynamics.

The paper focuses on the evaluation of hailstorms’ and thunderstorms winds’ events in the United States of America, in the period from 1996 to 2022, under the marked spatio-temporal self-exciting point processes point of view. The aim of the present article is the assessment and description of the spatio-temporal spontaneous and reproducing activity of severe hailstorms’ and thunderstorms winds’ processes. The present application shows how the spatio-temporal pattern is well-fitted and clearly explainable, according to the flexible semi-parametric ETAS model fitting.

Crime risk assessment needs tackling complex interrelationships between stochastic and deterministic components of spatio-temporal models. Criminal phenomena can be modeled using spatio-temporal point patterns of certain criminal data, and here we pay attention to the stochastic models of log-Gaussian Cox processes (LGCP) and self-exciting Hawkes processes (SEHP). We provide a comprehensive modeling strategy, combining both processes, noting that: (a) an LGCP facilitates the incorporation of first-order information through spatial and temporal deterministic components and second-order information through a stochastic component, and (b) a SEHP provides sufficient flexibility to incorporate various components in the background subprocess. To account for crime risk assessment, the deterministic components of the LGCP were estimated using a generalized linear model (GLM) for the temporal part, and a generalized additive model with B-splines for the highly nonlinear spatial covariates. In addition, the background rate components of the SEHP were estimated by a non-parametric stochastic reconstruction technique that includes a temporal periodicity, a separable spatial component, a long-term trend, and a semi-parametric method for the relaxation coefficients. MCMC-MALA and maximum likelihood were used for inference in both the LGCP and SEHP processes. We analyze crime events from the city of Riobamba (Ecuador), and with a complementary use of both stochastic point process models, we are able to assess the risk of crime, and provide reliable forecasts for weeks ahead.

Crime data analysis is an essential source of information to aid social and political decisions makers regarding the allocation of public security resources. Computer-aided dispatch systems and technological advances in geographic information systems have made analysing and visualising historical spatial and temporal records of crimes a vital part of police operations and strategy. We look at our motivating crime problem as a spatio-temporal point pattern. Using a conditional approach based on properties of Poisson point processes, we transform the spatio-temporal point process prediction problem into a classification problem. We create spatio-temporal handcrafted features to link future and past events and use machine learning algorithms to learn behavioural patterns from the data. The fitted model is then used to carry out the reverse transformation, i.e. to perform spatio-temporal risk predictions based on the outcomes of the classification problem. Our procedure has theoretical formalism from point process theory and gains flexibility and computational efficiency inherited from the machine learning field. We show its performance under some simulated scenarios and a real application to spatio-temporal prediction and risk assessment of homicides in Bogota, Colombia.