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.

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…

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…

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…

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.

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.

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…

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.

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.

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

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 methods for complex spatio-temporal point processes

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.

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.

A novel sequential testing procedure for selecting the number of changepoints in segmented regression models

In this work, we address the problem of selecting the number of changepoints in segmented regression models. We propose a novel stepwise procedure and assess its performance through simulation studies. We demonstrate that our proposal behaves well with the Gaussian and Binomial responses.

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.

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.