This work proposes χ^2-type test statistics to assess different hypotheses on the local structure of an observed marked point pattern. The test statistics is based on the local inhomogeneous extension of the mark-weighted K-function to investigate local behaviour of the marked point pattern. The summary statistic captures interactions between marks and locations by assessing local contributions to global deviations from independence or homogeneity. The methodology proves to be effective in identifying both global and localised departures from the null hypotheses, even in scenarios with subtle mark structures or small sample sizes. Real-world environmental applications to forestry and earthquake data demonstrate the utility of the proposed framework for detecting spatially dependent marked structures in the patterns.

Common practice in spatial point process modelling dictates that formal analysis begins with intensity estimation, which is carried out by exploiting external covariates, when available. Using this intensity estimate, one usually proceeds by obtaining non-parametric summary statistics estimates, in order to assess which model best fits the data. The state of the art in parametric intensity modelling is employing the Poisson likelihood function, but this underperforms when the data come from a more complex model, with some kind of interaction among points. Hence, to address this shortcoming, we propose a method that incorporates local second-order characteristics to account for spatial dependencies in the model fitting procedure. Our method relies on a locally weighted Poisson log-likelihood, which avoids making explicit assumptions about the type and degree of spatial interaction. We are therefore able to include external covariates while exploiting the non-parametric methods’ advantages, flexibly including second-order characteristics. We further propose a non-parametric test for the detection of interaction between points. Simulation studies demonstrate that the proposed method outperforms standard approaches in capturing diverse spatial interaction behaviours. An application to real forestry data further highlights the model’s flexibility in the presence of locally varying point interaction structures.

Likelihood-based inference for three-dimensional Poisson point processes requires numerical approximation of the integral term in the log-likelihood through a cubature scheme algorithm. The quality of this approximation, and hence the accuracy of the resulting statistical inference, depends on a small set of tuning parameters controlling the cubature construction. Despite their practical importance, the literature provides little guidance on how these parameters should be selected in order to obtain reliable first-order inference. This paper addresses this issue for purely spatial three-dimensional Poisson point process models. We formalize the cubature scheme in $ \mathbb {R}<^>3 $ R3 and conduct an extensive simulation study across multiple Poisson process scenarios, process sizes, and cubature configurations. Cubature settings are evaluated by combining parameter mean squared error with a second-order diagnostic based on the three-dimensional inhomogeneous K-function and the Global Envelope Test. The simulation results are then aggregated into empirically grounded practical recommendations for selecting the dummy-point ratio, the tessellation resolution, and the dummy-point layout. Finally, a real three-dimensional spatial application illustrates how cubature choices consistent with these recommendations can lead to stable parameter estimates, reliable fitted intensities, and satisfactory diagnostic performance.

stopp is a novel R package specifically designed for the analysis of spatio-temp oral point patterns which might have occurred in a subset of the Euclidean space or on some specific linear network, such as roads of a city. It represents the first package providing a comprehensive modeling framework for spatio-temp oral Poisson point processes. While many specialized models exist in the scientific literature for analyzing complex spatiotemp oral point patterns, we address the lack of general software for comparing simpler alternative models and their goodness of fit. The package's main functionalities include modeling and diagnostics, together with exploratory analysis tools and the simulation of point processes. A particular focus is given to local first-order and second-order characteristics. The package aggregates existing methods within one coherent framework, including those we proposed in recent papers, and it aims to welcome many further proposals and extensions from the R community.

In the analysis of spatial point patterns with associated real-valued marks, standard models either rely on strong distributional assumptions about the marks to incorporate their effect on the estimated intensity, or exclude them from the fitting procedure, studying the marks through marked summary statistics. In this article, we address this issue by proposing two approaches, one parametric and one semi-parametric, to model the intensity of marked point patterns with real-valued marks in two spatial dimensions, without making any assumption on the marks distribution. Both methods allow us to estimate the effect of the mark on the intensity of the process and the density of the mark across the observed window. We show that by including mark information in the model, when the real-valued mark has an impact on the intensity, we can obtain better intensity estimates with respect to unmarked models, giving an additional layer of information about the process.

Our study addresses the analysis of environmental concerns through point process theory. Among those, Sicily faced an escalating issue of uncontrolled fires in recent years, necessitating a thorough investigation into their spatio-temporal dynamics. Each fire is treated as a unique point in both space and time, allowing us to assess the influence of environmental and anthropogenic factors. A non-separable spatio-temporal Poisson model is applied to investigate the influence of land use types on fire distribution, controlling for other environmental covariates. The results highlight the significant effect of human activities, altitude, and slope on spatio-temporal fire occurrences, also confirming their dependence on various environmental variables, including the maximum daily temperature, wind speed, surface pressure, and total precipitation. As a model with constant parameters in space and time may be too restrictive, a local version of the proposed model is also fitted. This allows us to obtain better performance and more valuable insight into the estimated effects of the different environmental covariates on the occurrence of fires, which we find to vary both in time and space. This research work’s relevance lies in the analysis of an important environmental problem through complex point process models, yet easily interpretable, given their resemblance to regression-type models. We also provide reference to newly available open-source software for estimating such models. Finally, we contribute to the framework of spatio-temporal point process modelling by integrating data with different spatio-temporal resolutions from very diverse sources.

This study presents a statistical approach to accurately predict the effective temperatures of pre-main sequence stars, which are necessary for determining stellar ages using the isochrone methodology and cutting-age starspots-dependent models. By training a Neural Network model on high-quality spectroscopic temperatures from the Gaia-ESO Survey as the response variable, and using photometric data from Gaia DR3 and 2MASS catalogs as explanatory variables, we implemented a methodology to accurately derive the effective temperatures of much larger populations of stars for which only photometric data are available. The model demonstrated robust performance for low-mass stars with temperatures below 7 000 K, including young stars, the primary focus of this work. Predicted temperatures were employed to construct Hertzsprung-Russell diagrams and to predict stellar ages of different young clusters and star forming regions through isochrone interpolation, achieving excellent agreement with spectroscopic-based ages and literature values derived from model-independent methods like lithium equivalent widths. The inclusion of starspot evolutionary models improved the age predictions, providing a more accurate description of stellar properties. Additionally, the results regarding the effective temperature and age predictions of the young clusters provide evidence for intrinsic age spreads in the youngest clusters, suggesting multiple formation events over time.

In many applied fields, it may be of interest to evaluate mediational mechanisms occurring in spatial domains. The approaches proposed so far in the literature to address this issue deal with areal data and often consider linear models. In this paper, we propose an approach to assess mediation in the presence of geostatistical data by combining the integrated nested Laplace approximation (INLA) with a derivative-based approach for mediation analysis, which allows one to estimate indirect effects also in the case of nonlinear models. We investigate the effect of ignoring spatial processes in the mediator and the outcome models through a simulation study, focusing also on the case of correlated processes. To show the usefulness of our approach, we also provided an ecological application.

This paper aims to enhance the inference for spatial point processes' intensity function when complex interactions among points play a crucial role. We exploit local characteristics into the inferential procedure of maximising a regularised Poisson likelihood, penalised by the degree of interaction among points. The experiments conducted emphasize the importance of local second-order characteristics in improving inference for complex spatial point processes.

This study presents a machine learning approach to predict the effective temperatures and their accuracy of premain sequence stars, which are essential for deriving stellar ages through isochrone fitting and starspot-dependent evolutionary models. We trained a Neural Network on high-quality spectroscopic temperatures from the Gaia-ESO Survey, using Gaia DR3 and 2MASS photometry as input features. To estimate predictive uncertainty, we implemented a Neural Network with bootstrap procedure, where each model was warm-started using the parameters of an initial network trained on the full dataset with K-fold cross-validation. This allowed accurate and robust temperature predictions for large stellar populations lacking spectroscopic data, with strong performance in the lowtemperature regime. The predicted temperatures were used to build Hertzsprung-Russell diagrams and derive stellar ages of young clusters by starspot evolutionary models, achieving good agreement with spectroscopic benchmarks and independent methods, such as lithium equivalent widths.

While statistical methods and models for spatial point processes with scalar marks are rather well-established, their counterparts for functional marked spatio-temporal point processes remain in their infancy. As a result, this has become a growing research topic, driven by advances in data collection, storage, and availability. Representative instances include earthquake and hurricane data, which involve functional marks and exhibit self-exciting behaviour. We contribute to this emerging area by developing a marked functional Hawkes point process and applying the proposed model to analyse hurricane data in the Atlantic Basin.

In this study, we explore the cubature scheme procedure for modelling three-dimensional point patterns through Poisson point process models, a computational realm that remains under-explored. Through simulations, we give guidelines for choosing the number of cubes to partition the observed three-dimensional region, the number of dummy points to generate, and whether to simulate them regularly or casually in space. We apply this methodology to the real observed point pattern of young stars of the Gaia Archive.

Sicily encountered a growing challenge of wildfires in 2023, necessitating a thorough investigation into their spatio-temporal dynamics. Our study addresses this concern by applying a Poisson separable spatio-temporal point process model. We prove that the spatial occurrence of fires is influenced by human activities, altitude, and slope, while the temporal one is mainly due to environmental variables, including temperature, wind speed, surface pressure, and total precipitation.

Starting from the evaluation of presence-only data, and according to stochastic processes theory, we propose a classification method for unknown larval fish specimens, which is based on Local Indicators of Spatio-Temporal Association (LISTA). LISTA functions are typically used to evaluate the presence of clustered local second-order structures in spatio-temporal data. Here, these tools were applied to the classification of two rare species of mesopelagic fish larvae belonging to the genus Vinciguerria (V. attenuata and V. poweriae), detected in the Strait of Sicily, from 1998 to 2016. To evaluate the dependence of larval fish abundance spatio-temporal distributions from covariates, with the aim of understanding their impact on the reproducing activity of Vinciguerria spp., we fit a thinned inhomogeneous multitype spatio-temporal Poisson point process model. According to the goodness-of-fit evaluation, based on second-order diagnostics, the spatio-temporal Poisson point process model perfectly fits larval fish abundance’ presence-only data, after the classification procedure. We classify units representing spatio-temporal events by a LISTA functions-based classification procedure of local interaction. In addition, a stochastic processes’ model for the evaluation of presence-only data from an inferential point of view is estimated, accounting for covariates and sampling bias correction. The modeling analysis is carried out before and after the classification procedure, with the aim to evaluate the difference in terms of interpretation and diagnostics.

In 2023, Sicily faced an escalating issue of uncontrolled fires, necessitating a thorough investigation into their spatio-temporal dynamics. Our study addresses this concern through point process theory. Each wildfire is treated as a unique point in both space and time, allowing us to assess the influence of environmental and anthropogenic factors by fitting a spatio-temporal separable Poisson point process model, with a particular focus on the role of land usage. First, a spatial log-linear Poisson model is applied to investigate the influence of land use types on wildfire distribution, controlling for other environmental covariates. The results highlight the significant effect of human activities, altitude, and slope on spatial fire occurrence. Then, a Generalized Additive Model with Poisson-distributed response further explores the temporal dynamics of wildfire occurrences, confirming their dependence on various environmental variables, including the maximum daily temperature, wind speed, surface pressure, and total precipitation.

This work presents the cubature scheme for the fitting of spatio-temporal Poisson point processes. The methodology is implemented in the R Core Team (2024) package stopp (D'Angelo and Adelfio, 2023), published on the Comprehensive R Archive Network (CRAN) and available from https://CRAN.R-project.org/package=stopp. Since the number of dummy points should be sufficient for an accurate estimate of the likelihood, numerical experiments are currently under development to give guidelines on this aspect.

Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains. However, there remains a need to improve inference for complex intensity functions, especially when the point process likelihood is intractable and in the presence of interactions among points. This paper addresses this gap by proposing a method that exploits local second-order characteristics to account for local dependencies in the fitting procedure. Our approach utilises the Papangelou conditional intensity function for general Gibbs processes, avoiding explicit assumptions about the degree of interaction and homogeneity. We provide simulation results and an application to real data to assess the proposed method's goodness-of-fit. Overall, this work contributes to advancing statistical techniques for point process analysis in the presence of spatial interactions.

This collection of articles stems from the discussion on complex environmental data

Although there are recent developments for the analysis of first and second-order characteristics of point processes on networks, there are very few attempts in introducing models for network data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the background and the triggering components. Then we consider a semi-parametric version, including a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our model can be easily adapted to multi-type processes. Our network model outperforms a planar version, improving the fitting of the self-exciting point process model.