arXiv subjects

Jorge Mateu

Publications and source records attributed to Jorge Mateu.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Spatio-Temporal Dirichlet Process Mixture Model for Coronavirus Disease-19

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 posterior distribution of the parameters for the previous time step as the prior information for the current time step. This approach enables us to incorporate time dependence into our model in a computationally efficient manner without complicating the model structure. We also develop a model assessment by comparing the data with theoretical densities, and outline the goodness-of-fit of our fitted model.

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arXiv2022

Mapping the intensity function of a non-stationary point process in unobserved areas

Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets (e.g., earthquake prediction, seismic hazard...). In this context, a key aspect is how to map earthquakes density in seismogenic areas from censored data or even in areas that are not covered by the network. We propose to predict the spatial distribution of earthquakes from the knowledge of presence locations and geological relationships, taking into account any interaction between records. Namely, in a more general setting, we aim to estimate the intensity function of a point process, conditional to its censored realization, as in geostatistics for continuous processes. We define a predictor as the best linear unbiased combination of the observed point pattern. We show that the weight function associated to the predictor is the solution of a Fredholm equation of second kind. Both the kernel and the source term of the Fredholm equation are related to the first-and second-order characteristics of the point process through the intensity and the pair correlation function. Results are presented and illustrated on simulated non-stationary point processes and real data for mapping Greek Hellenic seismicity in a region with unreliable and incomplete records.

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arXiv2022

Nonparametric testing of the dependence structure among points-marks-covariates in spatial point patterns

We investigate testing of the hypothesis of independence between a covariate and the marks in a marked point process. It would be rather straightforward if the (unmarked) point process were independent of the covariate and the marks. In practice, however, such an assumption is questionable and possible dependence between the point process and the covariate or the marks may lead to incorrect conclusions. Therefore, we propose to investigate the complete dependence structure in the triangle points--marks--covariates together. We take advantage of the recent development of the nonparametric random shift methods, namely the new variance correction approach, and propose tests of the null hypothesis of independence between the marks and the covariate and between the points and the covariate. We present a detailed simulation study showing the performance of the methods and provide two theorems establishing the appropriate form of the correction factors for the variance correction. Finally, we illustrate the use of the proposed methods in two real applications.

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arXiv2022

ANOVA for Data in Metric Spaces, with Applications to Spatial Point Patterns

We give a review of recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is based on the classic Levene's test for detecting differences in dispersion. It uses only pairwise distances of data points and and can be computed quickly and precisely in situations where the computation of barycenters ("generalized means") in the data space is slow, only by approximation or even infeasible. We show the asymptotic normality of our test statistic and present simulation studies for spatial point pattern data, in which we compare the various procedures in a 1-way ANOVA setting. As an application, we perform a 2-way ANOVA on a data set of bubbles in a mineral flotation process.

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arXiv2022

Generalised functional additive mixed models with compositional covariates for areal Covid-19 incidence curves

We extend the generalised functional additive mixed model to include (functional) compositional covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a subspace of the $L^2$, we include functional compositions as transformed functional covariates with constrained effect function. The extended model allows for the estimation of linear, nonlinear 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.

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arXiv2021

A new class of spatial covariance functions generated by higher-order kernels

Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier transform of some higher-order kernels. Further, we extend this class of the spatial covariance functions to the spatio-temporal setting by using the idea used in Ma (2003).

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arXiv2021

Multivariate hierarchical analysis of car crashes data considering a spatial network lattice

Road traffic casualties represent a hidden global epidemic, demanding evidence-based interventions. This paper demonstrates a network lattice approach for identifying road segments of particular concern, based on a case study of a major city (Leeds, UK), in which 5,862 crashes of different severities were recorded over an eight-year period (2011-2018). We consider a family of Bayesian hierarchical models that include spatially structured and unstructured random effects, to capture the dependencies between the severity levels. Results highlight roads that are more prone to collisions, relative to estimated traffic volumes, in the northwest and south of city-centre. We analyse the Modifiable Areal Unit Problem (MAUP), proposing a novel procedure to investigate the presence of MAUP on a network lattice. We conclude that our methods enable a reliable estimation of road safety levels to help identify "hotspots" on the road network and to inform effective local interventions.

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arXiv2021

Bayesian Effect Selection for Additive Quantile Regression with an Analysis to Air Pollution Thresholds

Statistical techniques used in air pollution modelling usually lack the possibility to understand which predictors affect air pollution in which functional form; and are not able to regress on exceedances over certain thresholds imposed by authorities directly. The latter naturally induce conditional quantiles and reflect the seriousness of particular events. In the present paper we focus on this important aspect by developing quantile regression models further. We propose a general Bayesian effect selection approach for additive quantile regression within a highly interpretable framework. We place separate normal beta prime spike and slab priors on the scalar importance parameters of effect parts and implement a fast Gibbs sampling scheme. Specifically, it enables to study quantile-specific covariate effects, allows these covariates to be of general functional form using additive predictors, and facilitates the analysts' decision whether an effect should be included linearly, non-linearly or not at all in the quantiles of interest. In a detailed analysis on air pollution data in Madrid (Spain) we find the added value of modelling extreme nitrogen dioxide (NO2) concentrations and how thresholds are driven differently by several climatological variables and traffic as a spatial proxy. Our results underpin the need of enhanced statistical models to support short-term decisions and enable local authorities to mitigate or even prevent exceedances of NO2 concentration limits.

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arXiv2020

Spatio-temporal small area surveillance of the Covid-19 pandemics

The emergence of Covid-19 requires new effective tools for epidemiological surveillance. Spatio-temporal disease mapping models, which allow dealing with highly disaggregated spatial and temporal units of analysis, are a priority in this sense. Spatio-temporal models provide a geographically detailed and temporally updated overview of the current state of the pandemics, making public health interventions to be more effective. Moreover, the use of spatio-temporal disease mapping models in the new Covid-19 epidemic context, facilitates estimating newly demanded epidemiological indicators, such as the instantaneous reproduction number (R_t), even for small areas. This, in turn, allows to adapt traditional disease mapping models to these new circumstancies and make their results more useful in this particular context. In this paper we propose a new spatio-temporal disease mapping model, particularly suited to Covid-19 surveillance. As an additional result, we derive instantaneous reproduction number estimates for small areas, enabling monitoring this parameter with a high spatial disaggregation. We illustrate the use of our proposal with the separate study of the disease pandemics in two Spanish regions. As a result, we illustrate how touristic flows could haved shaped the spatial distribution of the disease. In these real studies, we also propose new surveillance tools that can be used by regional public health services to make a more efficient use of their resources.

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arXiv2020

A hierarchical spatio-temporal model to analyze relative risk variations of COVID-19: a focus on Spain, Italy and Germany

The novel coronavirus disease (COVID-19) has spread rapidly across the world in a short period of time and with a heterogeneous pattern. Understanding the underlying temporal and spatial dynamics in the spread of COVID-19 can result in informed and timely public health policies. In this paper, we use a spatio-temporal stochastic model to explain the temporal and spatial variations in the daily number of new confirmed cases in Spain, Italy and Germany from late February to mid September 2020. Using a hierarchical Bayesian framework, we found that the temporal trend of the epidemic in the three countries rapidly reached their peaks and slowly started to decline at the beginning of April and then increased and reached their second maximum in August. However decline and increase of the temporal trend seems to be sharper in Spain and smoother in Germany. The spatial heterogeneity of the relative risk of COVID-19 in Spain is also more pronounced than Italy and Germany.

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arXiv2020

Analyzing Car Thefts and Recoveries with Connections to Modeling Origin-Destination Point Patterns

For a given region, we have a dataset composed of car theft locations along with a linked dataset of recovery locations which, due to partial recovery, is a relatively small subset of the set of theft locations. For an investigator seeking to understand the behavior of car thefts and recoveries in the region, several questions are addressed. Viewing the set of theft locations as a point pattern, can we propose useful models to explain the pattern? What types of predictive models can be built to learn about recovery location given theft location? Can the dependence between theft locations and recovery locations be formalized? Can the flow between theft sites and recovery sites be captured? Origin-destination modeling offers a natural framework for such problems. However, here the data is not for areal units but rather is a pair of point patterns, with the recovery point pattern only partially observed. We offer modeling approaches for investigating the questions above and apply the approaches to two datasets. One is small from the state of Neza in Mexico with areal covariate information regarding population features and crime type. A second, much larger one, is from Belo Horizonte in Brazil but lacks covariates.

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arXiv2020

Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes

This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a unified framework for different types of spatio-temporal data including both, purely qualitatively (multivariate) cases and multivariate cases with additional quantitative marks. The proposed graphical model is defined through partial spectral density characteristics, it is highly computationally efficient and reflects the conditional similarity among sets of spatio-temporal sub-processes of either points or marked points with identical discrete marks. The paper considers three applications, two on crime data and a third one on forestry.

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arXiv2019

Functional marked point processes -- A natural structure to unify spatio-temporal frameworks and to analyse dependent functional data

This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent e.g. spatial paths or functions of time. To be able to consider e.g. multivariate FMPPs, we also attach an additional, Euclidean, mark to each point. We indicate how FMPPs quite naturally connect the point process framework with both the functional data analysis framework and the geostatistical framework. We further show that various existing models fit well into the FMPP framework. In addition, we introduce a new family of summary statistics, weighted marked reduced moment measures, together with their non-parametric estimators, in order to study features of the functional marks. We further show how they generalise other summary statistics and we finally apply these tools to analyse population structures, such as demographic evolution and sex ratio over time, in Spanish provinces.

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arXiv2019

Revisiting the random shift approach for testing in spatial statistics

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed causes that the assumption of exchangability, which is essential for the Monte Carlo test to be exact, is not fulfilled. We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor $1/n$. This corresponds to the asymptotic order of the variance of the test statistics. In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross $K$-function. Therefore we recommend it, when the point patterns are clustered, where the cross $K$-function achieves liberality.

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arXiv2019

Inhomogeneous higher-order summary statistics for linear network point processes

We introduce the notion of intensity reweighted moment pseudostationary point processes on linear networks. Based on arbitrary general regular linear network distances, we propose geometrically corrected versions of different higher-order summary statistics, including the inhomogeneous empty space function, the inhomogeneous nearest neighbour distance distribution function and the inhomogeneous $J$-function. We also discuss their non-parametric estimators. Through a simulation study, considering models with different types of spatial interaction, we study the performance of our proposed summary statistics. Finally, we make use of our methodology to analyse two datasets: motor vehicle traffic accidents and spider data.

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arXiv2019

Metrics and barycenters for point pattern data

We introduce the transport-transform (TT) and the relative transport-transform (RTT) metrics between finite point patterns on a general space, which provide a unified framework for earlier point pattern metrics, in particular the generalized spike time and the normalized and unnormalized OSPA metrics. Our main focus is on barycenters, i.e. minimizers of a $q$-th order Fréchet functional with respect to these metrics. We present a heuristic algorithm that terminates in a local minimum and is shown to be fast and reliable in a simulation study. The algorithm serves as an umbrella method that can be applied on any state space where an appropriate algorithm for solving the location problem for individual points is available. We present applications to geocoded data of crimes in Euclidean space and on a street network, illustrating that barycenters serve as informative summary statistics. Our work is a first step towards statistical inference in covariate-based models of repeated point pattern observations.

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arXiv2019

A spatial dependence graph model for multivariate spatial hybrid processes

This paper is concerned with the joint analysis of multivariate mixed-type spatial data, where some components are point processes and some are of lattice-type by nature. After a survey of statistical methods for marked spatial point and lattice processes, the class of multivariate spatial hybrid processes is defined and embedded within the framework of spatial dependence graph models. In this model, the point and lattice sub-processes are identified with nodes of a graph whereas missing edges represent conditional independence among the components. This finally leads to a general framework for any type of spatial data in a multivariate setting. We demonstrate the application of our method in the analysis of a multivariate point-lattice pattern on crime and ambulance service call-out incidents recorded in London, where the points are the locations of different pre-classified crime events and the lattice components report different aggregated incident rates at ward level.

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arXiv2019

Partial and semi-partial measures of spatial associations for multivariate lattice data

This paper concerns the development of partial and semi-partial measures of spatial associations in the context of multivariate spatial lattice data which describe global or local associations among spatially aggregated measurements for pairs of different components conditional on all remaining components. The new measures are illustrated using aggregated data on crime counts at ward level.

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