Including covariates in a space-time point process with application to seismicity

AbstractThe paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package

Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs

An estimation approach for the semi-param-etric intensity function of a class of space-time point processes is introduced. In particular we want to account for the estimation of parametric and nonparametric components simultaneously, applying a forward predictive likelihood to semi-parametric models. For each event, the probability of being a background event or an offspring is therefore estimated

Some extensions in space-time LGCP: application to earthquake data

In this paper we aim at studying some extensions of complex space-time models, useful for the description of earthquake data. In particular we want to focus on the Log-Gaussian Cox Process (LGCP, [1]) model estimation approach, with some results on global informal diagnostics. Indeed, in our opinion the use of Cox processes that are natural models for point process phenomena that are environmentally driven could be a new approach for the description of seismic events. These models can be useful in estimating the intensity surface of a spatio-temporal point process, in constructing spatially continuous maps of earthquake risk from spatially discrete data, and in real-time seismic activity surveillance. Moreover, covariate information varying in space-time can be considered into the LGCP model, providing complex models useful for a proper description of seismic events. LGCP is a Cox process with Λ = expS(x), where S is a Gaussian process. This construction has some advantages, related to the multivariate Normal distribution features, since the moment properties Λ(x) are inherited by the Cox process. In particular, both estimation and diagnostics, can deal with some higherorder properties [2], expressed for instance by the intensity and the pair correlation function of the LGCP

Space-Time Forecasting of Seismic Events in Chile

The aim of this work is to study the seismicity in Chile using the ETAS (epidemic type aftershock sequences) space‐time approach. The proposed ETAS model is estimated using a semi‐parametric technique taking into account the parametric and nonparametric components corresponding to the triggered and background seismicity, respectively. The model is then used to predict the temporal and spatial intensity of events for some areas of Chile where recent large earthquakes (with magnitude greater than 8.0 M) occurred

Spatio-temporal spread pattern of Covid-19 in Italy

This paper investigates the spatio-temporal spread pattern of Covid-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag-York-Molliè model and some spatio-temporal extensions are provided. This modelling framework, which includes a temporal component, allows to study the time evolution of the spread pattern among the 107 Italian provinces. The focus is on the effect of citizens’ mobility patterns, represented here by the three distinct phases of the Italian virus first wave, identified by the Italian government, also characterised by the lockdown period. Results show the effectiveness of the lockdown action and an inhomogeneous spatial trend that characterises the virus spread during the first wave. Furthermore, the results suggest that the temporal evolution of each province’s cases is independent of the temporal evolution of the other ones, meaning that the contagions and temporal trend may be caused by some province-specific aspects rather than by the subjects’ spatial movements

Functional Principal components direction to cluster earthquake waveforms

Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous transformations of observed discrete data (Chiodi, 1989). In this paper we combine the aim of finding clusters from a set of individual curves to the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data. We apply a classical clustering method to rotated data, according to the direction of maximum variance. A k-means clustering algorithm based on PCA rotation of data is proposed, as an alternative to methods that require previous interpolation of data based on splines or linear fitting (Garc´ıa- Escudero and Gordaliza (2005), Tarpey (2007), Sangalli et al. (2008)

Chapter Determinants of spatial intensity of stop locations on cruise passengers tracking data

This paper aims at analyzing the spatial intensity in the distribution of stop locations of cruise passengers during their visit at the destination through a stochastic point process modelling approach on a linear network. Data collected through the integration of GPS tracking technology and questionnaire-based survey on cruise passengers visiting the city of Palermo are used, to identify the main determinants which characterize their stop locations pattern. The spatial intensity of stop locations is estimated through a Gibbs point process model, taking into account for both individual-related variables, contextual-level information, and for spatial interaction among stop points. The Berman-Turner device for maximum pseudolikelihood is considered, by using a quadrature scheme generated on the network. The approach used allows taking into account the linear network determined by the street configuration of the destination under analysis. The results show an influence of both socio-demographic and trip-related characteristics on the stop location patterns, as well as the relevance of distance from the main attractions, and potential interactions among cruise passengers in stop configuration. The proposed approach represents both improvements from the methodological perspective, related to the modelling of spatial point process on a linear network, and from the applied perspective, given that better knowledge of the determinants of spatial intensity of visitors’ stop locations in urban contexts may orient destination management policy

Local Inhomogeneous Weighted Summary Statistics for Marked Point Processes

We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds of local dependence structures. We first derive some basic properties and show how these new statistical tools can be used to construct most existing summary statistics for (marked) point processes. We then propose a local test of random labeling. This procedure allows us to identify points, and consequently regions, where the random labeling assumption does not hold, for example, when the (functional) marks are spatially dependent. Through a simulation study we show that the test is able to detect local deviations from random labeling. We also provide an application to an earthquake point pattern with functional marks given by seismic waveforms

Functional Principal Components direction to cluster earthquake

Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous transformations of observed discrete data (Chiodi, 1989). In this paper we combine the aim of finding clusters from a set of individual curves to the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data. We apply a classical clustering method to rotated data, according to the direction of maximum variance. A k-means clustering algorithm based on PCA rotation of data is proposed, as an alternative to methods that require previous interpolation of data based on splines or linear fitting (García-Escudero and Gordaliza (2005), Tarpey (2007), Sangalli et al. (2008))

Hydrological post-processing based on approximate Bayesian computation (ABC)

[EN] This study introduces a method to quantify the conditional predictive uncertainty in hydrological post-processing contexts when it is cumbersome to calculate the likelihood (intractable likelihood). Sometimes, it can be difficult to calculate the likelihood itself in hydrological modelling, specially working with complex models or with ungauged catchments. Therefore, we propose the ABC post-processor that exchanges the requirement of calculating the likelihood function by the use of some sufficient summary statistics and synthetic datasets. The aim is to show that the conditional predictive distribution is qualitatively similar produced by the exact predictive (MCMC post-processor) or the approximate predictive (ABC post-processor). We also use MCMC post-processor as a benchmark to make results more comparable with the proposed method. We test the ABC post-processor in two scenarios: (1) the Aipe catchment with tropical climate and a spatially-lumped hydrological model (Colombia) and (2) the Oria catchment with oceanic climate and a spatially-distributed hydrological model (Spain). The main finding of the study is that the approximate (ABC post-processor) conditional predictive uncertainty is almost equivalent to the exact predictive (MCMC post-processor) in both scenarios.This study was partially supported by the Departamento del Huila Scholarship Program No. 677 (Colombia) and Colciencias, by the Spanish Research Project TETIS-MED (ref. CGL2014-58127-C3-3-R) and TETIS-CHANGE (ref.RTI2018-093717-B-I00). Also, G. Adelfio's research has been supported by the national grant of the Italian Ministry of Education University and Research (MIUR) for the PRIN-2015 program, "Complex space-time modelling and functional analysis for probabilistic forecast of seismic events'. 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