Multidimensional Clustering and Registration of Seismic Waveform Data

Kernel estimation and display of a five-dimensional conditional intensity function

The aim of this paper is to find a convenient and effective method of displaying some second order properties in a neighbourhood of a selected point of the process. The used techniques are based on very general high-dimensional nonparametric smoothing developed to define a more gen- eral version of the conditional intensity function introduced in earlier earthquake studies by Vere-Jones (1978). 1976) is commonly used for such a purpose in discussing the cumulative behavior of interpoint distances about an initial point. It is defined as the expected number of events falling within a given distance of the initial event, divided by the overall density (rate in 2-dimensions) of the process, sa…

Further considerations on a new indicator for higher education student performance

Il presente lavoro si inserisce nel dibattito internazionale sul sistema di voto universitario e sulla sua sintesi come misura della performance di uno studente. Partendo dalla nuova misura proposta in Adelfio et al. (2014), in questo breve articolo si pone l’enfasi sull’importanza della scelta della misura opportuna, soprattutto nella individuazione delle possibili determinanti della performance, utile nella scelte delle opportune politiche di intervento sulla performance della carriera dello studente. Per richiamare il nuovo indicatore proposto e per fare il confronto con quello esistente, si `e fatto riferimento ai Sistema Universitario italiano. This paper joins the international debate…

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…

Minimum contrast for point processes' first-order intensity estimation

In this paper, we exploit some theoretical results, from which we know the expected value of the K-function weighted by the true first-order intensity function of a point pattern. This theoretical result can serve as an estimation method for obtaining the parameter estimates of a specific model, assumed for the data. The only requirement is the knowledge of the first-order intensity function expression, completely avoiding writing the likelihood, which is often complex to deal with in point process models. We illustrate the method through simulation studies for spatio-temporal point processes.

Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes

We propose a new fitting method to estimate the set of second-order parameters for the class of homogeneous spatio-temporal log-Gaussian Cox point processes. With simulations, we show that the proposed minimum contrast procedure, based on the spatio-temporal pair correlation function, provides reliable estimates and we compare the results with the current available methods. Moreover, the proposed method can be used in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. We describe earthquake sequences comparing several Cox model specifications.

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.

Gamma kernel intensity estimation in time point processes

Second-order diagnostics for space-time point processes with application to seismic events

A diagnostic method for space-time point process is introduced and used to interpret and assess the goodness of fit of particular models to real data such as the seismic ones. The proposed method is founded on the definition of a weighted process and allows to detect second-order features of data, like long-range dependence and fractal behavior, that are not accounted for by the fitted model. Applications to earthquake data are provided. Copyright © 2008 John Wiley & Sons, Ltd.

Migration and students' performance: detecting geographical differences following a curves clustering approach

Students’ migration mobility is the new form of migration: students migrate to improve their skills and become more valued for the job market. The data regard the migration of Italian Bachelors who enrolled at Master Degree level, moving typically from poor to rich areas. This paper investigates the migration and other possible determinants on the Master Degree students’ performance. The Clustering of Effects approach for Quantile Regression Coefficients Modelling has been used to cluster the effects of some variables on the students’ performance for three Italian macro-areas. Results show evidence of similarity between Southern and Centre students, with respect to the Northern ones.

An algorithm for earthquakes clustering based on maximum likelihood

In this paper we propose a clustering technique set up to separate and find out the two main components of seismicity: the background seismicity and the triggered one. We suppose that a seismic catalogue is the realization of a non homogeneous space-time Poisson clustered process, with a different parametrization for the intensity function of the Poisson-type component and of the clustered (triggered) component. The method here proposed assigns each earthquake to the cluster of earthquakes, or to the set of independent events, according to the increment to the likelihood function, computed using the conditional intensity function estimated by maximum likelihood methods and iteratively chang…

A new approach for clustering of effects in quantile regression

In this paper we aim at nding similarities among the coefficients from a multivariate regression. Using a quantile regression coefficients modeling, the effect of each covariate, given a response (also multivariate) is a curve in the multidimensional space of the percentiles. Collecting all the curves, describing the effects of each covariate on each response variable, we could be able to assess if only one or more covariates have same effects on different responses.

Testing for local structure in spatiotemporal point pattern data

The detection of clustering structure in a point pattern is one of the main focuses of attention in spatiotemporal data mining. Indeed, statistical tools for clustering detection and identification of individual events belonging to clusters are welcome in epidemiology and seismology. Local second-order characteristics provide information on how an event relates to nearby events. In this work, we extend local indicators of spatial association (known as LISA functions) to the spatiotemporal context (which will be then called LISTA functions). These functions are then used to build local tests of clustering to analyse differences in local spatiotemporal structures. We present a simulation stud…

Un metodo per l'identificazione di cluster di eventi sismici. 23° Convegno G.N.G.T.S (Roma 2004)

Some properties and applications of local second-order characteristics for spatio-temporal point processes on networks

Point processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this work, 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 also show that these LISTA functions are useful for diagnostics of models specified on the networks, and can be helpful to assess the goodness-of-fit of different s…

ETAS Space–Time Modeling of Chile Triggered Seismicity Using Covariates: Some Preliminary Results

Chilean seismic activity is one of the strongest in the world. As already shown in previous papers, seismic activity can be usefully described by a space–time branching process, such as the ETAS (Epidemic Type Aftershock Sequences) model, which is a semiparametric model with a large time-scale component for the background seismicity and a small time-scale component for the triggered seismicity. The use of covariates can improve the description of triggered seismicity in the ETAS model, so in this paper, we study the Chilean seismicity separately for the North and South area, using some GPS-related data observed together with ordinary catalog data. Our results show evidence that the use of s…

GLM-based automatic picking of waveforms

Identification and modeling of stop activities at the destination from GPS tracking data

Il presente articolo ha lo scopo di analizzare il comportamento turistico a destinazione, con un focus specifico sulle soste effettuate dai turisti nella destinazione. Vengono analizzati dati desunti da dispositivi GPS raccolti su un campione di crocieristi, a partire dai quali e possibile individuare le soste a destinazione `attraverso l’impiego di un opportuno algoritmo. L’effetto delle caratteristiche sociodemografiche e legate all’itinerario intrapreso sul numero di soste effettuate viene studiato attraverso l’impiego di modelli di reggressione di Poisson. I risultati sono di interesse sia da un punto di vista metodologico, legato all’analisi e sintesi di dati GPS, che dal punto di vist…

Inhomogeneous spatio-temporal point processes on linear networks for visitors’ stops data

We analyse the spatio-temporal distribution of visitors' stops by touristic attractions in Palermo (Italy) using theory of stochastic point processes living on linear networks. We first propose an inhomogeneous Poisson point process model, with a separable parametric spatio-temporal first-order intensity. We account for the spatial interaction among points on the given network, fitting a Gibbs point process model with mixed effects for the purely spatial component. This allows us to study first-order and second-order properties of the point pattern, accounting both for the spatio-temporal clustering and interaction and for the spatio-temporal scale at which they operate. Due to the strong d…

FLP estimation of semi-parametric models for space-time point processes and diagnostic tools

Abstract The conditional intensity function of a space–time branching model is defined by the sum of two main components: the long-run term intensity and short-run term one. Their simultaneous estimation is a complex issue that usually requires the use of hard computational techniques. This paper deals with a new mixed estimation approach for a particular space–time branching model, the Epidemic Type Aftershock Sequence model. This approach uses a simultaneous estimation of the different model components, alternating a parametric step for estimating the induced component by Maximum Likelihood and a non-parametric estimation step, for the background intensity, by FLP (Forward Predictive Like…

Hybrid kernel estimates of space-time earthquake occurrence rates using the Etas model

The following steps are suggested for smoothing the occurrence patterns in a clustered space–time process, in particular the data from an earthquake catalogue. First, the original data is fitted by a temporal version of the ETAS model, and the occurrence times are transformed by using the cumulative form of the fitted ETAS model. Then the transformed data (transformed times and original locations) is smoothed by a space–time kernel with bandwidth obtained by optimizing a naive likelihood cross-validation. Finally, the estimated intensity for the original data is obtained by back-transforming the estimated intensity for the transformed data. This technique is used to estimate the intensity f…

Local indicators of spatio-temporal association on linear networks

In this work, we extend the Local Indicators of Spatio-Temporal Association (LISTA) functions (Siino et al. 2018) to the non-Euclidean space of linear networks. We introduce the local version of some inhomogeneous second-order statistics for spatio-temporal point processes on linear networks (Morandi and Mateu, 2019), namely the K-function and the pair correlation function. Following the work of Adelfio et al. (2019) for the Euclidean case, we employ the proposed LISTA functions to assess the goodness-of-fit of different spatio-temporal models fitted to point patterns occurring on linear networks. Indeed, the peculiar lack of homogeneity in a network discourages the usage of traditional spa…

Un metodo per l’identificazione di clusters di eventi sismici

Marked Hawkes processes for Twitter data

In this paper, we propose to model retweet event sequences using a marked Hawkes process, which is a self-exciting point process where the occurrence of previous events in time increases the probability of further events. The aim is to analyse Twitter data combining temporal point processes theory and textual analysis. Since each retweet event carries a set of properties, we mark the process by different characteristics drawn from the textual analysis, finding that the tone of the description of the Twitter user is a good predictor of the number of retweets in a single cascade.

Analysis and assessment of trace element contamination in offshore sediments of the Augusta Bay (SE Sicily): A multivariate statistical approach based on canonical correlation analysis and mixture density estimation approach

Abstract An application of multivariate statistical methods is provided to identify anthropogenic contaminants and lithogenic elements in offshore sediments collected near the heavily industrialized Augusta Bay, Sicily. An exploratory statistical technique, based on canonical correlation analysis (CCA) and mixture density estimation approach, is used for distinguishing between natural and anthropogenic contributions of trace elements in the investigated sediments. Following the intensive industrialization of Augusta area, marine sediments reveal the severe impact of local anthropogenic activities for many elements (e.g. As, Cd, Hg, Pb, and Sb), which are considered very dangerous for the en…

Point process diagnostics based on weighted second-order statistics and their asymptotic properties

A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.

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 …

Evaluating the performance of a new picking algorithm based on the variance piecewise constant models

In this paper, a new picking algorithm for the automatic seismogram onset time determination is tested on a dataset of simulated waveforms. We aim at capturing the variations in the performance due to some characteristics of both the seismic event and its detection, which in turn affect some characteristics of the waveforms. We therefore simulate seismic events with different magnitude, and assumed to be detected with different distances from the nearest seismic station. Our tests permit to highlight the scenarios most suitable for our algorithm.

A distribution curves comparison approach to analyze the university moving students performance

Da qualche anno anche l’Italia sta assistendo a un flusso migratorio di studenti, che da un povero Sud si dirige verso un più ricco Nord. Se un tempo la migrazione avveniva nel momento di cercare lavoro, adesso questa è anticipata da studenti che ritengono di avere meggiore successo se conseguono il titolo al Nord. L’obiettivo di questo studio è verificare la sensazione empirica secondo la quale in realtà gli studenti che restano per iscriversi alla Laurea Magistrale hanno un percorso simile rispetto a quelli che si iscrivono a un percorso magistrale del Nord. Considerate diverse misure di performance, e svolto i confronti attraverso una nuova procedura di raffronto tra curve di distribuzio…

Mixed estimation technique in semi-parametric space-time point processes for earthquake description

An estimation approach for the semi-parametric intensity function of a particular space-time point process 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 one belonging to a seismic sequence is therefore estimated.

Mixed Non-Parametric and Parametric Estimation Techniques in R Package etasFLP for Earthquakes’ Description

etasFLP is an R package which fits an epidemic type aftershock sequence (ETAS) model to an earthquake catalog; non-parametric background seismicity can be estimated through a forward predictive likelihood approach, while parametric components of triggered seismicity are estimated through maximum likelihood; estimation steps are alternated until convergence is obtained and for each event the probability of being a background event is estimated. The package includes options which allow its wide use. Methods for plot, summary and profile are defined for the main output class object. The paper provides examples of the package's use with description of the underlying R and Fortran routines.

Degree course change and student performance: a mixed-effect approach

This paper focuses on students credits earning speed over time and its determinants, dealing with the huge percentage of students who do not take the degree within the legal duration in the Italian University System. A new indicator for the performance of the student career is proposed on real data, concerning the cohort of students enrolled at a Faculty of the University of Palermo (followed for 7 years). The new indicator highlights a typical zero-inflated distribution and suggests to investigate the effect of the degree course (DC) change on the student career. A mixed-effect model for overdispersed data is considered, with the aim of taking into account the individual variability as wel…

Windowed Etas Models With Application To The Chilean Seismic Catalogs

Abstract The seismicity in Chile is estimated using an ETAS (Epidemic Type Aftershock sequences) space–time point process through a semi-parametric technique to account for the estimation of parametric and nonparametric components simultaneously. The two components account for triggered and background seismicity respectively, and are estimated by alternating a ML estimation for the parametric part and a forward predictive likelihood technique for the nonparametric one. Given the geographic and seismological characteristics of Chile, the sensitivity of the technique with respect to different geographical areas is examined in overlapping successive windows with varying latitude. A different b…

Local characteristics of functional marked point processes with applications to seismic data

We present a family of local inhomogeneous mark-weighted summary statistics for general marked point processes. These capture various types of local dependence structures depending on the specified involved weight function. We use them to propose a local random labeling test. This procedure enables us to identify points and thus regions where the random labeling assumption does not hold, for example, when the (functional) marks are spatially dependent. We further present an application to a seismic point pattern with functional marks provided by seismic waveforms. Indeed, despite the relatively long history of point process theory, few approaches to analyzing spatial point patterns where th…

Gamma Kernel Intensity Estimation in Temporal Point Processes

In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.

Forward likelihood-based predictive approach for space-time point processes

Dealing with data from a space–time point process, the estimation of the conditional intensity function is a crucial issue even if a complete definition of a parametric model is not available. In particular, in case of exploratory contexts or if we want to assess the adequacy of a specific parametric model, some kind of nonparametric estimation procedure could be useful. Often, for these purposes kernel estimators are used and the estimation of the intensity function depends on the estimation of bandwidth parameters. In some fields, like for instance the seismological one, predictive properties of the estimated intensity function are pursued. Since a direct ML approach cannot be used, we pr…

A PCA-based clustering algorithm for the identification of stratiform and convective precipitation at the event scale: an application to the sub-hourly precipitation of Sicily, Italy

AbstractUnderstanding the structure of precipitation and its separation into stratiform and convective components is still today one of the important and interesting challenges for the scientific community. Despite this interest and the advances made in this field, the classification of rainfall into convective and stratiform components is still today not trivial. This study applies a novel criterion based on a clustering approach to analyze a high temporal resolution precipitation dataset collected for the period 2002–2018 over the Sicily (Italy). Starting from the rainfall events obtained from this dataset, the developed methodology makes it possible to classify the rainfall events into f…

Diagnostics for nonparametric estimation in space-time seismic processes

In this paper we propose a nonparametric method, based on locally variable bandwidths kernel estimators, to describe the space-time variation of seismic activity of a region of Southern California. The flexible estimation approach is introduced together with a diagnostic method for space-time point process, based on the interpretation of some second-order statistics, to analyze the dependence structure of observed data and suggest directions for fit improvement. In this paper we review a diagnostic method for space-time point processes based on the interpretation of the transformed version of some second-order statistics. The method is useful to analyze dependence structures of observed dat…

Regression quantiles to assess higher education performance

From 2001 Italian university system has adopted the credits to mea- sure the workload of the students. The weighted mean of marks with credits as weights is used to measure the their performance. In our opinion it does not seem a proper way to measure. We suggest to adopt the median of the weighted marks, because we are considering an ordinale variable, with a non-normal empir- ical distribution, and a®ected by outliers. Then, instead of using an OLS multiple regression, we investigate the determinants of the performance measured by the median using a regression quantile for ordinal response. A real dataset concerning 133 students of the Faculty of Economics of the University of Palermo is …

Clustering of waveforms-data based on FPCA direction

The necessity of nding similar features of waveforms data recorded for earthquakes at di erent time instants is here considered, since eventual similarity between these functions could suggest similar behavior of the source process of the corresponding earthquakes. In this paper we develop a clustering algorithm for curves based on directions de ned by an application of PCA to functional data.

Weighted local second-order statistics for complex spatio-temporal point processes

Spatial, temporal, and spatio-temporal point processes, and in particular Poisson processes, are stochastic processes that are largely used to describe and model the distribution of a wealth of real phenomena. When a model is fitted to a set of random points, observed in a given multidimensional space, diagnostic measures are necessary to assess the goodness-of-fit and to evaluate the ability of that model to describe the random point pattern behaviour. The main problem when dealing with residual analysis for point processes is to find a correct definition of residuals. Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data in…

Statistical Analysis of Macroseismic Data for a better Evaluation of Earthquakes Attenuation Laws

In this work we propose a statistical approach, based on the joint analysis of macroseismic data of Italian seismic events of the last two centuries, with which we obtain simultaneously maximum likelihood estimates of attenuation laws and coordinates of hypocenters. Our first results encourage us to use in the future more complex models, with a larger number of historical earthquakes.

Kernel intensity for space-time point processes with application to seismological problems

Dealing with data coming from a space-time inhomogeneous process, there is often the need of semi-parametric estimates of the conditional intensity function; isotropic or anisotropic multivariate kernel estimates can be used, with windows sizes h. The properties of the intensities estimated with this choice of h are not always good for specific fields of application; we could try to choose h in order to have good predictive properties of the estimated intensity function. Since a direct ML approach cannot be followed, we propose an estimation procedure, computationally intensive, based on the subsequent increments of likelihood obtained adding an observation at time. The first results obtain…

Integreating geological and seismological data in point process models for seismical analysis

Nowadays in the seismic and geological fields, large and complex data sets are available. This information is a valuable source that can be used for improving the seismic hazard assessment of a given region. In particular, the integration of geologic variables into point process models to study seismic pattern is an open research field that has not been fully explored. In this work, we present several open-access datasets (the catalogue of the earthquakes, geological information such as faults, plate boundary and the presence of volcanoes) that are properly treated to describe the seismicity of events occurred in Greece between 2005 and 2014. We use these datasets to fit an advanced spatial…

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 Gordali…

Nonparametric clustering of seismic events

In this paper we propose a clustering technique, based on the maximization of the likelihood function defined from the generalization of a model for seismic activity (ETAS model, (Ogata (1988))), iteratively changing the partitioning of the events. In this context it is useful to apply models requiring the distinction between independent events (i.e. the background seismicity) and strongly correlated ones. This technique develops nonparametric estimation methods of the point process intensity function. To evaluate the goodness of fit of the model, from which the clustering method is implemented, residuals process analysis is used.

Local Spatio-Temporal Log-Gaussian Cox Processes for seismic data analysis

We propose a local version of the spatio-temporal log-Gaussian Cox processes (LGCPs) employing the Local Indicators of Spatio-Temporal Association (LISTA) functions into the minimum contrast procedure to obtain space as well as time-varying parameters. We resort to the joint minimum contrast method fitting method to estimate the set of second-order parameters for the class of Spatio-Temporal LGCPs. We employ the proposed methodology to analyse real seismic data occurred Greece between 2004 and 2015.

Detection of spatio-temporal local structure on seismic data

For the description of the seismicity of an area, the comparison between local features of background and induced events could be a new perspective of research. In spatio-temporal point process, local second-order statistics provide information on the relationships of each event and its nearby events. In this paper, we use a test based on local indicators of spatio-temporal association (LISTA functions) for identifying different local structures comparing the two previous sets of events. We present a simulation study on the test and show the main results of the application on Greece earthquake data.

Stima semi-parametrica della funzione di intensità di un processo di punto spazio-temporale.

Nonparametric intensity estimation in space-time point processes and application to seismological problems

Statistical model diagnostics for earthquakes data

Selecting the Kth nearest-neighbour for clutter removal in spatial point processes through segmented regression models

We consider the problem of feature detection, in the presence of clutter in spatial point processes. A previous study addresses the issue of the selection of the best nearest neighbour for clutter removal. We outline a simple workflow to automatically estimate the number of nearest neighbours by means of segmented regression models applied to an entropy measure of cluster separation. The method is suitable for a feature with clutter as two superimposed Poisson processes on any twodimensional space, including linear networks. We present simulations to illustrate the method and an application to the problem of seismic fault detection.

FPCA Algorithm For Waveform Clustering

Similar features between waveform data recorded for earthquakes at different time instants could suggest similar behavior of the source process of the corresponding source seismic process. In this paper we combine the aim of finding clusters from a set of individual waveform curves with the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data. This approach overcome the limitation of the cross-correlation, and represents an alternative to methods based on the interpolation of data by splines or linear fitting.

Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity

Earthquakes are one of the most destructive natural disasters and the spatial distribution of their epi- centres generally shows diverse interaction structures at different spatial scales. In this paper, we use a multi-scale point pattern model to describe the main seismicity in the Hellenic area over the last 10 years. We analyze the interaction between events and the relationship with geo- logical information of the study area, using hybrid models as proposed by Baddeley et al. ( 2013 ). In our analysis, we find two competing suitable hybrid models, one with a full parametric structure and the other one based on nonpara- metric kernel estimators for the spatial inhomogeneity.

IMPLEMENTAZIONE DI UN ALGORITMO DI CLUSTERING PER L’IDENTIFICAZIONE DELLE PRECIPITAZIONI STRATIFORMI E CONVETTIVE ALLA SCALA D’EVENTO: UN’APPLICAZIONE ALLE PRECIPITAZIONI SUB-ORARIE DELLA SICILIA

Spatio-temporal analysis of the Covid-19 spread in Italy by Bayesian hierarchical models

In this paper, we investigate the spatio-temporal spread pattern of the virus Covid-19 in Italy, during the first wave of infections, from February to October 2020. We provide a disease mapping of the virus infections, by using the Besag-Yorke-Molliè model and its spatio-temporal extensions. Our results confirm the effectiveness of the lockdown action, and show that, during the first wave, the virus spread by an inhomogeneous spatial trend and each province was characterised by a specific temporal trend, independent of the temporal evolution of the observed cases in the other provinces

Some properties of local weighted second-order statistics for spatio-temporal point processes

Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the…

Earthquakes clustering interpretation based on a second-order diagnostic approach

Relazioni tra sismicita’ e tettonica nel margine settentrionale della Sicilia

Sea Surface Temperature Effects on the Mediterranean Marine Ecosystem: a Semiparametric Model Approach

Ocean warming is a worldwide phenomenon. The mean temperature of the catch (MTC) is becoming one of the leading indicators to assess the impact of sea surface temperature on fish communities. In this study, we apply a semiparametric regression approach to the MTC of the catches from MEDITS bottom trawl program in the Strait of Sicily (Central Mediterranean Sea) for the period 1995 to 2018 to evaluate the effects of climate change on continental shelf fish community. All covariates included in the model have a significant impact on the MTC level. Notably, the sea surface temperature (SST) effect on the MTC depends on depth, being positive near the surface and negative at the bottom.

An integrated approach to investigate the seismotectonics of northern Sicily and southern Tyrrhenian

Abstract This paper deals with a comparison among recent structure and seismicity in the hinge zone between northern Sicily and southern Tyrrhenian, corresponding to both emerged and submerged northern portion of the Maghrebian chain. This hinge zone is part of a wider W–E trending right-lateral shear zone, mainly characterized by both a synthetic NW-SE/W–E oriented, and antithetic left-lateral N–S/NE-SW fault systems, which has been affecting the tectonic edifice, since the Pliocene. The inland structures have been mapped using aerial-photo interpretation, geological mapping and mesostructural analysis to reconstruct the stress regime in the study area. On the contrary, the offshore struct…

Efficient change point detection in genomic sequences of continuous measurements

Abstract Motivation: Knowing the exact locations of multiple change points in genomic sequences serves several biological needs, for instance when data represent aCGH profiles and it is of interest to identify possibly damaged genes involved in cancer and other diseases. Only a few of the currently available methods deal explicitly with estimation of the number and location of change points, and moreover these methods may be somewhat vulnerable to deviations of model assumptions usually employed. Results: We present a computationally efficient method to obtain estimates of the number and location of the change points. The method is based on a simple transformation of data and it provides re…

ETAS Space time modelling of Chile induced seismicity using covariates.

<p>Chilean seismic activity is among the strongest ones in the world. As already shown in previous papers, seismic activity can be usefully described by a space-time branching process, like the ETAS (Epidemic Type Aftershock Sequences) model, which is a semiparametric model with a large time scale component for the background seismicity and a small time scale component for the induced seismicity. The large-scale component intensity function  is usually estimated by  nonparametric techniques, specifically in our paper we used the Forward Likelihood Predictive approach (FLP); the induced seismicity is modelled with a parametric space-time function. In c…

Hints of latent drivers investigating university student performance

Job market, nowadays, asks for higher and higher skills and competences. Therefore, also the measurement and assessment of the university students performance are crucial issues for policy makers. Although the scientific literature provides several papers investigating the main determinants of university student performance, often results are very different, and they seem to hold just in very specific contexts. This paper aims to contribute to the international literature, focusing on the role of student specific characteristics, supporting the idea that unobservable variables (such as motivation, aptitudes or abilities) should be more investigated.

Maximum Likelihood Based Declustering of Simulated and Observed Seismic Catalogs

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–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which includes a temporal component, allows the studying of 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 characterized by the lockdown period. Results show the effectiveness of the lockdo…

Study of the interaction structure of the East Sicily Seismicity: global and local scale.

Financial contagion through space-time point processes

AbstractWe propose to study the dynamics of financial contagion by means of a class of point process models employed in the modeling of seismic contagion. The proposal extends network models, recently introduced to model financial contagion, in a space-time point process perspective. The extension helps to improve the assessment of credit risk of an institution, taking into account contagion spillover effects.

Local inhomogeneous second-order characteristics for spatio-temporal point processes occurring on linear networks

AbstractPoint 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 diagn…

Classification of spatio-temporal point pattern in the presence of clutter using K-th nearest neighbour distances

In a point process spatio-temporal framework, we consider the problem of features detection in the presence of clutters. We extend the methodology of Byers and Raftery (1998) to the spatio-temporal context by considering the properties of the K-th nearest-neighbour distances. We make use of the spatio-temporal distance based on the Euclidean norm where the temporal term is properly weighted. We show the form of the probability distributions of such K-th nearest-neighbour distance. A mixture distribution, whose parameters are estimated with an EM algorithm, is used to classify points into clutters or features. We assess the performance of the proposed approach with a simulation study, togeth…

Locally weighted spatio-temporal minimum contrast for Log-Gaussian Cox Processes

We propose a local version of the spatio-temporal log-Gaussian Cox processes (LGCPs) employing the Local Indicators of Spatio-Temporal Association (LISTA) functions into the minimum contrast procedure to obtain space as well as time-varying parameters. We resort to the joint minimum contrast method fitting method to estimate the set of second-order parameters for the class of spatio-temporal LGCPs. This approach has the advantage of being usable in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field (GRF).

Earthquakes clustering based on maximum likelihood estimation of point process conditional intensity function

Clustering and Registration of Multidimensional Functional Data

In order to find similarity between multidimensional curves, we consider the application of a procedure that provides a simultaneous assignation to clusters and alignment of such functions. In particular we look for clusters of multivariate seismic waveforms based on EM-type procedure and functional data analysis tools.

Comparison between nonparametric and parametric estimate of the conditional intensity function of a seismic space-time point process

A seismic gap can be defined as a segment of an active geologic fault that has not produced seismic events for an unusually long time; gaps are often considered susceptible to future strong earthquakes occurrence and therefore their identification may be useful for predictive purposes. In this paper we try to identify gaps in an area of South Tyrrhenian Sea by comparing the observed seismicity, estimated by nonparametric method, and the theoretical one, described by a particular space-time point process (ETAS model).

A fast and efficient picking algorithm for earthquake early warning application based on the variance piecewise constant models

An earthquake warning system, or earthquake early warning system, is a system of accelerometers, seismometers, communication, computers, and alarms that is devised for notifying adjoining regions of a substantial earthquake while it is in progress. This is not the same as earthquake prediction, which is currently incapable of producing decisive event warnings. The implementation of efficient and computationally simple picking algorithm is necessary for this purpose, as well as automatic picking of seismic phases for seismic surveillance and routine earthquake location for fast hypocenter determination. In this paper a method for picking based on the detection of signals changes in variance …

A new picking algorithm based on the variance piecewise constant models

AbstractIn this paper, we propose a novel picking algorithm for the automatic P- and S-waves onset time determination. Our algorithm is based on the variance piecewise constant models of the earthquake waveforms. The effectiveness and robustness of our picking algorithm are tested both on synthetic seismograms and real data. We simulate seismic events with different magnitudes (between 2 and 5) recorded at different epicentral distances (between 10 and 250 km). For the application to real data, we analyse waveforms from the seismic sequence of L’Aquila (Italy), in 2009. The obtained results are compared with those obtained by the application of the classic STA/LTA picking algorithm. Althoug…

Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes

A local version of spatio-temporal log-Gaussian Cox processes is proposed by using Local Indicators of Spatio-Temporal Association (LISTA) functions plugged into the minimum contrast procedure, to obtain space as well as time-varying parameters. The new procedure resorts to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. Simulation studies to assess the performance of the proposed fitting procedure are presented, and an application to seismic spatio-temporal point pattern…

Testing for local structure in spatiotemporal point pattern data

The detection of clustering structure in a point pattern is one of the main focuses of attention in spatiotemporal data mining. Indeed, statistical tools for clustering detection and identification of individual events belonging to clusters are welcome in epidemiology and seismology. Local second-order characteristics provide information on how an event relates to nearby events. In this work, we extend local indicators of spatial association (known as LISA functions) to the spatiotemporal context (which will be then called LISTA functions). These functions are then used to build local tests of clustering to analyse differences in local spatiotemporal structures. We present a simulation stud…

Spatio-temporal classification in point patterns under the presence of clutter

Local Spatial Log-Gaussian Cox Processes for seismic data

AbstractIn this paper, we propose the use of advanced and flexible statistical models to describe the spatial displacement of earthquake data. The paper aims to account for the external geological information in the description of complex seismic point processes, through the estimation of models with space varying parameters. A local version of the Log-Gaussian Cox processes (LGCP) is introduced and applied for the first time, exploiting the inferential tools in Baddeley (Spat Stat 22:261–295, 2017), estimating the model by the local Palm likelihood. We provide methods and approaches accounting for the interaction among points, typically described by LGCP models through the estimation of th…

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

In this paper, we exploit a result in point process theory, knowing the expected value of the $K$-function weighted by the true first-order intensity function. This theoretical result can serve as an estimation method for obtaining the parameters estimates of a specific model, assumed for the data. The motivation is to generally avoid dealing with the complex likelihoods of some complex point processes models and their maximization. This can be more evident when considering the local second-order characteristics, since the proposed method can estimate the vector of the local parameters, one for each point of the analysed point pattern. We illustrate the method through simulation studies for…

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 labelling. This procedure allows us to identify points, and consequently regions, where the random labelling assumption does not hold, e.g.~when the (functional) marks are spatially dependent. Through a simulatio…

Clustering of waveforms based on FPCA direction

Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous transformations of observed discrete data (Chiodi, 1989). Waveforms correlation techniques have been introduced to charac- terize the degree of seismic event similarity (Menke, 1999) and in facilitating more accurate relative locations within similar event clusters by providing more precise timing of seismic wave (P and S) arrivals (Phillips, 1997). In this paper functional analysis (Ramsey, and Silverman, 2006) is considered to highlight common characteristics of waveforms-data and to summarize these charac- teristics by few components, by applying a variant of a classical clust…

Time-Frequency Filtering for Seismic Waves Clustering

This paper introduces a new technique for clustering seismic events based on processing, in time-frequency domain, the waveforms recorded by seismographs. The detection of clusters of waveforms is performed by a k-means like algorithm which analyzes, at each iteration, the time-frequency content of the signals in order to optimally remove the non discriminant components which should compromise the grouping of waveforms. This step is followed by the allocation and by the computation of the cluster centroids on the basis of the filtered signals. The effectiveness of the method is shown on a real dataset of seismic waveforms.

Self-exciting point process modelling of crimes on linear networks

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 mode…

Spatio‐temporal classification in point patterns under the presence of clutter

We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. In previous studies, related to the spatial context, Kth nearest-neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation-maximization algorithm. This paper extends this methodology to the spatio-temporal context by considering the properties of the spatio-temporal Kth nearest-neighbor distances. For this purpose, we make use of a couple of spatio-temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions o…

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.

Un tentativo di analisi integrata della tettonica e sismicità nella zona di cerniera tra Sicilia settentrionale e Basso Tirreno.

Clusters of effects curves in quantile regression models

In this paper, we propose a new method for finding similarity of effects based on quantile regression models. Clustering of effects curves (CEC) techniques are applied to quantile regression coefficients, which are one-to-one functions of the order of the quantile. We adopt the quantile regression coefficients modeling (QRCM) framework to describe the functional form of the coefficient functions by means of parametric models. The proposed method can be utilized to cluster the effect of covariates with a univariate response variable, or to cluster a multivariate outcome. We report simulation results, comparing our approach with the existing techniques. The idea of combining CEC with QRCM per…

Flexible space-time process for seismic data

Point processes are well studied objects in probability theory and a powerful tool in statistics for modelling and analyzing the distribution of real phenomena, such as the seismic one. Point processes can be specified mathematically in several ways, for instance, by considering the joint distributions of the counts of points in arbitrary sets or defining a complete intensity function. The conditional intensity function is a function of the point history and it is itself a stochastic process depending on the past up to time t. In this paper some techniques to estimate the intensity function of space-time point processes are developed, by following semi-parametric approaches and diagnostic m…

Assessing local differences between the spatio-temporal second-order structure of two point patterns occurring on the same linear network

Abstract We introduce Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks and use them to build a statistical test for local second-order structure. This allows to identify differences in the spatio-temporal clustering behaviour of two point patterns, a point pattern of interest and a background one, both occurring on the same linear network. We assess the performance of the testing procedure for local second-order structure through simulation studies under a variety of scenarios that also account for different generating point processes. We show that the proposed local test is able to correctly identify the spatio-temporal difference in the local second-ord…

Semi-parametric estimation of the intensity function in space-time point processes

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.

Development and testing of seismic regional discriminants

Local test of random labelling for functional marked point processes

We introduce the local t-weighted marked nth-order inhomogeneous K-function, in a Functional Marked Point Processes framework. We employ the proposed summary statistics to run a local test of random labelling, useful to identify points, and consequently regions, where this assumption does not hold, i.e. the functional marks are spatially dependent.

Semi-parametric estimation of conditional intensity functions in inhomogeneous space-time point processes

Dealing with data coming from a space-time inhomogeneous process, there is often the need of obtaining estimates of the conditional intensity function, without a complete defi nition of a parametric model and so nonparametric estimation is required: isotropic or anisotropic kernel estimates can be used. The properties of the intensities estimated are not always good, expecially in seismological field. We could try to choose the bandwidth in order to have good predictive properties of the estimated intensity function. Since a direct ML approach can not be followed, we use an estimation procedure based on the further increments of likelihood obtained adding a new observation. Similarly to cro…

Southern-Tyrrhenian seismicity in space-time-magnitude domain

An analysis is conducted on a catalogue containing more than 2000 seismic events
 occurred in the southern Tyrrhenian Sea between 1988 and October 2002, as an attempt
 to characterise the main seismogenetic processes active in the area in space, time and magnitude domain by means of the parameters of phenomenological laws.
 
 We chose to adopt simple phenomenological models, since the low number of data did
 not allow to use more complex laws.
 
 The two main seismogenetic volumes present in the area were considered for the purpose
 of this work. The first includes a nearly homogeneous distribution of hypocentres in a
 NW steeply dipping layer as far as a…

University student talent: the real driver for performance?

Investigation about the university student performance, and its measurement, are very crucial issues for any policy maker. Since the economic crisis, jobs market requires even higher skills and competences. Literature offers a lot of papers about the university student quality and performance, in order to identify the main determinants of them. Often, results are very different, and they seems to hold just in a specific context. This paper aims to investigate the role of a latent variable that can take into account the student motivation, aptitude, and abilities, here conveniently called talent. A random effect Quantile Regression on a new measure of Italian student performance has been ado…

Residual analysis for space-time earthquakes occurrence models

Simultaneous seismic wave clustering and registration

In this paper we introduce a simple procedure to identify clusters of multivariate waveforms based on a simultaneous assignation and alignment procedure. This approach is aimed at the identification of clusters of earthquakes, assuming that similarities between seismic events with respect to hypocentral parameters and focal mechanism correspond to similarities between waveforms of events. Therefore we define a distance measure between seismic curves in R^d d>=1, in order to interpret and better understand the main features of the generating seismic process.

The student talent in a random effects Quantile Regression Model for university performance

This paper is a development of a previous work on performance of Italian university students. A Quantile Regression was carried out on a proposed performance indicator, based on a transformation of the median of the marks weighted by credits. Results suggested to investigate the role of students peculiar features on their performance, measured by the transformation of the weighted marks. Therefore, a random intercept Quantile Regression model is fitted on real data concerning graduates over the legal university duration set in Italy, enrolled in 2002 in two Degree Courses of the University of Palermo. Results show that the student performance seems to be influenced by the student's aptitude…

Clustering of seismic catalogs based on maximum likelihood estimation

Probabilistic forecast for Northern New Zealand seismic process: a kernel-based approach

Forecast of earthquakes of a given area of Northern New Zealand is provided. It is based on the assumption that future earthquakes activity may be based on the smoothing of past earthquakes. Therefore, seismic activity is described by an intensity function factorized into kernel functions which depend on time longitude and latitude of events.

Depth-based methods for clustering of functional data.

The problem of detecting clusters is a common issue in the analysis of functional data and some interesting intuitions from approaches relied on depth measures can be considered for construction of basic tools for clustering of curves. Motivated by recent contributions on the problem clustering and alignment of functional data, we also consider the problem of aligning a set of curves when classification procedures are implemented. The variability among curves can be interpreted in terms of two components, phase and amplitude; phase variability, or misalignment, can be eliminated by aligning the curves, according to a similarity index and a warping function. Some approaches address the misal…

Probabilistic Forecast for Northern New Zealand Seismic Process Based on a Forward Predictive Kernel Estimator

In seismology predictive properties of the estimated intensity function are often pursued. For this purpose, we propose an estimation procedure in time, longitude, latitude and depth domains, based on the subsequent increments of likelihood obtained adding an observation one at a time. On the basis of this estimation approach a forecast of earthquakes of a given area of Northern New Zealand is provided, assuming that future earthquakes activity may be based on the smoothing of past earthquakes.

An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach

A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.

Space-Time FPCA Clustering of Multidimensional Curves.

In this paper we focus on finding clusters of multidimensional curves with spatio-temporal structure, applying a variant of a k-means algorithm based on the principal component rotation of data. The main advantage of this approach is to combine the clustering functional analysis of the multidimensional data, with smoothing methods based on generalized additive models, that cope with both the spatial and the temporal variability, and with functional principal components that takes into account the dependency between the curves.

Seismic sequences identification in Italy by local test of random labelling

Spatio-Temporal Linear Network Point Processes for GPS Data Analysis

This work aims at analyzing the spatio-temporal intensity in the distribution of stop locations of cruise passengers during their visit at the destination. Data are collected through the integration of GPS tracking technology and questionnaire-based survey on a sample of cruise passengers visiting the city of Palermo (Italy), and they are used to identify the main determinants which characterize cruise passengers’ stop locations pattern. The spatio-temporal distribution of visitors' stops is analysed by mean of the theory of stochastic point processes occurring on linear networks, in order to consider the street configuration of the city and the location of the main attractions. First, an i…

Hawkes processes on networks for crime data

Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatio-temporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for both the background and the triggering components, and then we include a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our network model outperforms a planar version, improving the fitting of the self-exciting point process model.

Spatial seismic point pattern analysis with Integrated Nested Laplace Approximation

This paper proposes the use of Integrated Nested Laplace Approximation (Rue et al., 2009) to describe the spatial displacement of earthquake data. Specifying a hiechical structure of the data and parameters, an inhomogeneuos Log-Gaussian Cox Processes model is applied for describing seismic events occurred in Greece, an area of seismic hazard. In this way, the dependence of the spatial point process on external covariates can be taken into account, as well as the interaction among points, through the estimation of the parameters of the covariance of the Gaussian Random Field, with a computationally efficient approach.

Community detection of seismic point processes

In this paper, we combine robin and Local Indicators of Spatio-Temporal Association (LISTA) functions. robin is an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability. We use it to propose a classification algorithm of events in a spatio-temporal point pattern, by means of the local second-order characteristics and the community detection procedure in network analysis. We demonstrate the proposed procedure on a real data analysis on seismic data.

Point processes residual analysis and asymptotical distribution of transformed versions of some second-order statistics

An approach to hypothesis testing based on local indicators of spatio-temporal association

The detection of clustering structure in a point pattern is one of the major focus of attention in spatio-temporal data mining. For instance, statistical tools for clustering detection and identification of events belonging to clusters are welcome in epidemiology and seismology. Local second-order statistics can provide information on how an event relates to nearby events. We extend local indicators of spatial association (known as LISA functions) into the spatio-temporal context (which then will be called LISTA functions). These functions can be used for local tests in the context of case-control spatio-temporal point patterns, and are able to assess in the neighbourhood of each event if t…

An improved detection of clusters in complex ecological systems by using the Ripley’s K-function

Change-points detection for variance piecewise constant models

A new approach based on the fit of a generalized linear regression model is introduced for detecting change-points in the variance of heteroscedastic Gaussian variables, with piecewise constant variance function. This approach overcome some limitations of both exact and approximate well-known methods that are based on successive application of search and tend to overestimate the real number of changes in the variance of the series. The proposed method just requires the computation of a gamma GLM with log-link, resulting in a very efficient algorithm even with large sample size and many change points to be estimated.

Towards the specification of a self-exciting point process for modelling crimes in Valencia

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.

Spatio-temporal log-Gaussian Cox processes on earthquake events

This work presents an application of spatio-temporal log-Gaussian Cox processes for the description of earthquake events. To explain the overall spatial trend, spatial geological information in the study area such as faults and volcanoes are introduced in the model. Moreover, an anisotropic specification of the covariance matrix of the Gaussian process is used to improve the explanation of the phenomenon. We apply and compare different models to explain the seismic events occurred in Alaska over the last decades.

Statistical Picking of Multivariate Waveforms

In this paper, we propose a new approach based on the fitting of a generalized linear regression model in order to detect points of change in the variance of a multivariate-covariance Gaussian variable, where the variance function is piecewise constant. By applying this new approach to multivariate waveforms, our method provides simultaneous detection of change points in functional time series. The proposed approach can be used as a new picking algorithm in order to automatically identify the arrival times of P- and S-waves in different seismograms that are recording the same seismic event. A seismogram is a record of ground motion at a measuring station as a function of time, and it typica…

Space-time FPCA Algorithm for clustering of multidimensional curves.

In this paper we focus on finding clusters of multidimensional curves with spatio-temporal structure, applying a variant of a k-means algorithm based on the principal component rotation of data. The main advantage of this approach is to combine the clustering functional analysis of the multidimensional data, with smoothing methods based on generalized additive models, that cope with both the spatial and the temporal variability, and with functional principal components that takes into account the dependency between the curves.

Semiparametric estimation of conditional intensity functions for space-time processes

When dealing with data coming from a space time inhomogeneous process, there is often the need of obtaining reliable estimates of the conditional intensity function. According to the field of application, intensity function can be estimated through some assessed parametric model, where parameters are estimated by Maximum Likelihood method. If we are only in an exploratory context or we would like to assess the adequacy of the parametric model, some kind of nonparametric estimation is required. Often, isotropic or anisotropic kernel estimates can be used, e.g. using the Silverman rule for the choice of the windows sizes h (Silverman, 1986). When the purpose of the study is the estimation of …

Local LGCP estimation for spatial seismic processes

Using recent results for local composite likelihood for spatial point processes, we show the performance of advanced and flexible statistical models to describe the spatial displacement of earthquake data. Local models described by Baddeley (2017) allow for the possibility of describing both seismic catalogs and sequences. When analysing seismic sequences, the analysis of the small scale variation is the main issue. The interaction among points is taken into account by Log-Gaussian Cox Processes models through the estimation of the parameters of the covariance of the Gaussian Random Field. In their local version these parameters are allowed to vary spatially, and this is a crucial aspect fo…

Un metodo per l'identificazione di cluster di eventi sismici

A method to identify clusters of seismic events

Classification in point patterns on linear networks under clutter

The problem of features detection under present of clutter in point process on linear networks establishes a methodological and computational challenge with multiple kind of applications as traffic accidents among other. Previous works related to the same topical but developed in more simpler geometries tackles the issue of the clutter removal through the distance of nearest-neighbour and show good results with high classification rates. We extend this procedure to the linear networks motivated by the classification of the traffic accidents on the road network of a city. Simulations demonstrate the performance of the method.

Comparing local structures of spatio-temporal point processes on linear networks

We employ the Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks to build a statistical test for local second-order structure. This allows to identify differences in the spatio-temporal clustering behaviour of two point patterns, a point pattern of interest and a background one, both occurring on the same linear network. We illustrate the proposed methodology analysing a traffic-related problem.

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 sim…