Jorge Mateu

The supplementary material summarises the results obtained when testing the spatial predictive accuracy considering different time periods and alternative training sets. Moreover, it includes additional details on the comparison with planar and separable modelling approaches. Finally, we also report more precise details regarding the computing times on the extended road network.

We extend the generalized functional additive mixed model to include compositional and functional compositional (density) covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a sub-space of the , we include functional compositions as transformed functional covariates with constrained yet interpretable effect function. The extended model allows for the estimation of linear, non-linear, and time-varying effects of scalar and functional covariates, as well as (correlated) functional random effects, in addition to the compositional effects. We use the model to estimate the effect of the age, sex, and smoking (functional) composition of the population on regional Covid-19 incidence data for Spain, while accounting for climatological and socio-demographic covariate effects and spatial correlation.

The inhomogeneous Log-Gaussian Cox Process (LGCP) defines a flexible point process model for the analysis of spatial point patterns featuring inhomogeneity/spatial trend and aggregation patterns. To fit an LGCP model to spatial point pattern data and study the spatial trend, one could link the intensity function with continuous spatial covariates. Although non-continuous covariates are becoming more common in practice, the existing estimation methods so far only cover covariates in continuous form. As a consequence, to implement such methods, the non-continuous covariates are replaced by the continuous ones by applying some transformation techniques, which are many times problematic. In this paper, we develop a technique for inhomogeneous LGCP involving non-continuous covariates, termed piecewise constant covariates. The method does not require covariates transformation and likelihood …

We use data on imprisonment in Spain to fit a system of three ordinary differential equations that describes the temporal evolution of three different groups in the country: offenders that are not in prison, offenders that are in prison, and the rest of people. These remaining people are considered as susceptible, who may become offenders by their relationships. That is, crime is regarded to behave as a social epidemic. We first investigate the dynamics of the model to find out when criminality becomes extinct or endemic in the long run, depending on the basic reproduction number. Then, we estimate the parameters of the model and conduct a sensitivity analysis. Finally, a random error is incorporated, and nonlinear regression is carried out to gather the unexplained variability of the data. Our results report a satisfactory model fitting to the crime data, closely delineating their dynamics.

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.

La Flavescencia Dorada de la vid es una enfermedad causada por un fitoplasma que actualmente representa una seria amenaza, siendo objeto de intensa investigación debido a su considerable impacto socioeconómico. Aunque no existen actualmente métodos curativos para combatir la enfermedad, se ha implementado un control preventivo e indirecto centrado en su vector, Scaphoideus titanus. Este artículo aborda varios factores que afectan a la transmisión de la enfermedad, focalizándose en la biología del vector, su monitoreo y los momentos óptimos de tratamiento.

DiscussionThe authors are to be congratulated on a valuable and thought-provoking contribution. Deep neural network models have become increasingly prominent across many domains of science, engineering, and industry, finding applications in almost every field. These models have proven particularly valuable when dealing with data exhibiting spatial dependencies (such as images) or temporal dependencies (as in this paper). There is growing interest in combining the ideas and approaches from deep machine learning and neural networks with spatial statistical methods, to capitalize on the expressiveness that deep machine learning models often provide, and/or to approximate intractable or computationally difficult aspects of a well-accepted statistical procedure (Wikle et al., 2023).

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.

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.

Self‐exciting point processes allow modeling the temporal location of an event of interest, considering the history provided by previously observed events. This family of point processes is commonly used in several areas such as criminology, economics, or seismology, among others. The standard formulation of the self‐exciting process implies assuming that the underlying stochastic process is dependent on its previous history over the entire period under analysis. In this paper, we consider the possibility of modeling a point pattern through a point process whose structure is not necessarily of self‐exciting type at every instant or temporal interval. Specifically, we propose a mixture point process model that allows the point process to be either self‐exciting or homogeneous Poisson, depending on the instant within the study period. The performance of this model is evaluated both through a simulation study and a …

This paper proposes a new methodology for detecting outliers in spatially correlated functional data. We use a Local Correlation Integral (LOCI) algorithm substituting the Euclidean distance calculation by the Hilbert space distance weighted by the semivariogram, obtaining a weighted dissimilarity metric among the geo-referenced curves, which takes into account the spatial correlation structure. In addition, we also consider the distance proposed in Romano et al.(2020), which optimizes the distance calculation for spatially dependent functional data. A simulation study is conducted to evaluate the performance of the proposed methodology. We analyze the role of a threshold value appearing as an hyperparameter in our approach, and show that our distance weighted by the semivariogram is overall superior to the other types of distances considered in the study. We analyze time series of Land Surface …

Understanding the spatio‐temporal patterns of the coronavirus disease 2019 (COVID‐19) is essential to construct public health interventions. Spatially referenced data can provide richer opportunities to understand the mechanism of the disease spread compared to the more often encountered aggregated count data. We propose a spatio‐temporal Dirichlet process mixture model to analyze confirmed cases of COVID‐19 in an urban environment. Our method can detect unobserved cluster centers of the epidemics, and estimate the space‐time range of the clusters that are useful to construct a warning system. Furthermore, our model can measure the impact of different types of landmarks in the city, which provides an intuitive explanation of disease spreading sources from different time points. To efficiently capture the temporal dynamics of the disease patterns, we employ a sequential approach that uses the …

A number of papers have dealt with the analysis of crime data using self-exciting point process theory after the analogy drawn between aftershock ETAS models and crime rate. With the aim to describe crime events that occurred in Valencia in the last decade, in this paper, we justify the need for a self-exciting point process model through spatial and temporal exploratory analysis.

We study the dynamics of abstract models for crime evolution. The population is divided into three compartments, taking into account the participation in crime and incarceration. Individuals transit between the three segments, assuming that having more contact with criminally active people increases one's risk of learning and acquiring the same traits; essentially, crime is regarded as a social epidemic. In the literature, there are several models of this type, based on spatial homogeneity and ordinary differential equations. However, these ideas have not been extended to account for spatial variability. Here, we achieve this target with discrete and continuous forms of space: patch and reaction–diffusion compartmental systems, respectively. We build the models and focus on the effect of the basic reproduction number on the long‐term dynamics of crime (persistence or disappearance). Several theoretical results are …

Spatial dependence into environmental data is an influential criterion in clustering processes, as the resulting clustering outputs depend very much upon such spatial structure. As classical methods do not take spatial dependence in consideration, the inclusion of this structure produces unexpected but more realistic results and clusters of curves that may not be similar in shape or behavior. In this paper, clustering is made using the KMSCFD algorithm for spatially correlated functional data. The methodology was developed through weighting the distance matrix between the curves with the trace‐variogram calculated with the coefficients of the basis functions resulting from a data smoothing operation. For the validation of the method, a number of simulated scenarios were tested together with an application to Normalized Difference Vegetation Index data derived from a high elevation ecosystem in the Ecuadorian …

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.

Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and spatial point processes yield a highly challenging instance of such modern spatial data applications. Indeed, the analysis of spatial random point configurations, where the point attributes themselves are functions rather than scalar-valued quantities, is just in its infancy, and extensions to function-valued quantities still remain limited. In this view, we extend current existing first- and second-order summary characteristics for real-valued point attributes to the case where in addition to every spatial point location a set of distinct function-valued quantities are available. Providing a flexible treatment of more complex point process scenarios, we build a framework to consider points with multivariate function-valued marks, and develop sets of different cross-function (cross-type and also multi-function cross-type) versions of summary characteristics that allow for the analysis of highly demanding modern spatial point process scenarios. We consider estimators of the theoretical tools and analyse their behaviour through a simulation study and two real data applications.

Point processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this paper, we extend Local Indicators of Spatio-Temporal Association (LISTA) functions to the non-Euclidean space of linear networks, allowing to obtain information on how events relate to nearby events. In particular, we propose the local version of two inhomogeneous second-order statistics for spatio-temporal point processes on linear networks, the K- and the pair correlation functions. We put particular emphasis on the local K-functions, deriving come theoretical results which enable us to show that these LISTA functions are useful for diagnostics of models specified on networks, and can be helpful to assess the goodness-of-fit of different spatio-temporal models fitted to point patterns occurring on linear networks. Our methods do not rely on any particular model …

Detecting change-points in multivariate settings is usually carried out by analyzing all marginals either independently, via univariate methods, or jointly, through multivariate approaches. The former discards any inherent dependencies between different marginals and the latter may suffer from domination/masking among different change-points of distinct marginals. As a remedy, we propose an approach which groups marginals with similar temporal behaviors, and then performs group-wise multivariate change-point detection. Our approach groups marginals based on hierarchical clustering using distances which adjust for inherent dependencies. Through a simulation study we show that our approach, by preventing domination/masking, significantly enhances the general performance of the employed multivariate change-point detection method. Finally, we apply our approach to two datasets: (i) Land Surface …

This work focuses on kernel estimation of the pair correlation function (PCF) for inhomogeneous spatial point processes. We propose a bootstrap bandwidth selector based on minimizing the mean integrated squared error (MISE). The variance term is estimated by nonparametric bootstrap, and the bias by a plug-in approach using a pilot estimator of the PCF. Kernel estimators of the PCF also require a pilot estimator of the first-order intensity. We test the performance of the bandwidth selector and the role of the pilot intensity estimator in a simulation study. The bootstrap bandwidth selector is competitive with cross-validation procedures, but the contribution of the bandwidth parameter to the goodness-of-fit of the kernel PCF estimator is minor in comparison with that of the pilot intensity function. The data-based kernel intensity estimator leads to biased kernel PCF estimators, while both kernel and parametric covariate …