arXiv subjects

Nicoletta D'Angelo

Publications and source records attributed to Nicoletta D'Angelo.

16 recordsLinked to original sources

arXiv2026

Testing the Structural Properties of Marked Point Processes Using Local Inhomogeneous Mark-Weighted K-Functions

This work proposes $χ^2$-type test statistics to assess different hypotheses on the local structure of an observed marked point pattern. The test statistics is based on the local inhomogeneous extension of the mark-weighted $K$-function to investigate local behaviour of the marked point pattern. The summary statistic captures interactions between marks and locations by assessing local contributions to global deviations from independence or homogeneity. The methodology proves to be effective in identifying both global and localised departures from the null hypotheses, even in scenarios with subtle mark structures or small sample sizes. Real-world environmental applications to forestry and earthquake data demonstrate the utility of the proposed framework for detecting spatially dependent marked structures in the patterns.

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arXiv2025

Detecting changes in space-varying parameters of local Poisson point processes

Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated spatial regression, a novel framework that extends segmented regression models to spatial point processes, with the aim of detecting abrupt changes in the effect of external covariates onto the process intensity. Our approach consists of two main steps. First, we apply a spatial segmentation algorithm to geographically weighted regression estimates, generating different tessellations that partition the study area into regions where model parameters can be assumed constant. Next, we fit log-linear Poisson models in which covariates interact with the tessellations, enabling region-specific parameter estimation and classical inferential procedures, such as hypothesis testing on regression coefficients. Unlike geographically weighted regression, our approach allows for discrete changes in regression coefficients, making it possible to capture abrupt spatial variations in the effect of real-valued spatial covariates. Furthermore, the method naturally addresses the problem of locating and quantifying the number of detected spatial changes. We validate our methodology through simulation studies and applications to two examples where a model with region-wise parameters seems appropriate and to an environmental dataset of earthquake occurrences in Greece.

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arXiv2024

A point process approach for the classification of noisy calcium imaging data

We study noisy calcium imaging data, with a focus on the classification of spike traces. As raw traces obscure the true temporal structure of neuron's activity, we performed a tuned filtering of the calcium concentration using two methods: a biophysical model and a kernel mapping. The former characterizes spike trains related to a particular triggering event, while the latter filters out the signal and refines the selection of the underlying neuronal response. Transitioning from traditional time series analysis to point process theory, the study explores spike-time distance metrics and point pattern prototypes to describe repeated observations. We assume that the analyzed neuron's firing events, i.e. spike occurrences, are temporal point process events. In particular, the study aims to categorize 47 point patterns by depth, assuming the similarity of spike occurrences within specific depth categories. The results highlight the pivotal roles of depth and stimuli in discerning diverse temporal structures of neuron firing events, confirming the point process approach based on prototype analysis is largely useful in the classification of spike traces.

q-bio.NC↗

arXiv2024

stopp: An R Package for Spatio-Temporal Point Pattern Analysis

stopp is a novel R package specifically designed for the analysis of spatio-temporal point patterns which might have occurred in a subset of the Euclidean space or on some specific linear network, such as roads of a city. It represents the first package providing a comprehensive modelling framework for spatio-temporal Poisson point processes. While many specialized models exist in the scientific literature for analyzing complex spatio-temporal point patterns, we address the lack of general software for comparing simpler alternative models and their goodness of fit. The package's main functionalities include modelling and diagnostics, together with exploratory analysis tools and the simulation of point processes. A particular focus is given to local first-order and second-order characteristics. The package aggregates existing methods within one coherent framework, including those we proposed in recent papers, and it aims to welcome many further proposals and extensions from the R community.

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arXiv2024

Testing for a general changepoint in psychometric studies: changes detection and sample size planning

This paper introduces a new method for change detection in psychometric studies based on the recently introduced pseudo Score statistic, for which the sampling distribution under the alternative hypothesis has been determined. Our approach has the advantage of simplicity in its computation, eliminating the need for resampling or simulations to obtain critical values. Additionally, it comes with a known null/alternative distribution, facilitating easy calculations for power levels and sample size planning. The paper indeed also discusses the topic of power analysis in segmented regression, namely the estimation of sample size or power level when the study data being collected focuses on a covariate expected to affect the mean response via a piecewise relationship with an unknown breakpoint. We run simulation results showing that our method outperforms other Tests for a Change Point (TFCP) with both normally distributed and binary data and carry out a real SAT Critical reading data analysis. The proposed test contributes to the framework of psychometric research, and it is available on the Comprehensive R Archive Network (CRAN) and in a more user-friendly Shiny App, both illustrated at the end of the paper.

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arXiv2024

Semi-parametric profile pseudolikelihood via local summary statistics for spatial point pattern intensity estimation

Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains. However, there remains a need to improve inference for complex intensity functions, especially when the point process likelihood is intractable and in the presence of interactions among points. This paper addresses this gap by proposing a method that exploits local second-order characteristics to account for local dependencies in the fitting procedure. Our approach utilises the Papangelou conditional intensity function for general Gibbs processes, avoiding explicit assumptions about the degree of interaction and homogeneity. We provide simulation results and an application to real data to assess the proposed method's goodness-of-fit. Overall, this work contributes to advancing statistical techniques for point process analysis in the presence of spatial interactions.

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arXiv2024

Cubature scheme for spatio-temporal Poisson point processes estimation

This work presents the cubature scheme for the fitting of spatio-temporal Poisson point processes. The methodology is implemented in the R Core Team (2024) package stopp (D'Angelo and Adelfio, 2023), published on the Comprehensive R Archive Network (CRAN) and available from https://CRAN.R-project.org/package=stopp. Since the number of dummy points should be sufficient for an accurate estimate of the likelihood, numerical experiments are currently under development to give guidelines on this aspect.

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arXiv2024

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

In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

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arXiv2024

A machine learning approach to predict university enrolment choices through students' high school background in Italy

This paper explores the influence of Italian high school students' proficiency in mathematics and the Italian language on their university enrolment choices, specifically focusing on STEM (Science, Technology, Engineering, and Mathematics) courses. We distinguish between students from scientific and humanistic backgrounds in high school, providing valuable insights into their enrolment preferences. Furthermore, we investigate potential gender differences in response to similar previous educational choices and achievements. The study employs gradient boosting methodology, known for its high predicting performance and ability to capture non-linear relationships within data, and adjusts for variables related to the socio-demographic characteristics of the students and their previous educational achievements. Our analysis reveals significant differences in the enrolment choices based on previous high school achievements. The findings shed light on the complex interplay of academic proficiency, gender, and high school background in shaping students' choices regarding university education, with implications for educational policy and future research endeavours.

cs.LG↗

arXiv2024

Spatio-temporal point process modelling of fires in Sicily exploring human and environmental factors

In 2023, Sicily faced an escalating issue of uncontrolled fires, necessitating a thorough investigation into their spatio-temporal dynamics. Our study addresses this concern through point process theory. Each wildfire is treated as a unique point in both space and time, allowing us to assess the influence of environmental and anthropogenic factors by fitting a spatio-temporal separable Poisson point process model, with a particular focus on the role of land usage. First, a spatial log-linear Poisson model is applied to investigate the influence of land use types on wildfire distribution, controlling for other environmental covariates. The results highlight the significant effect of human activities, altitude, and slope on spatial fire occurrence. Then, a Generalized Additive Model with Poisson-distributed response further explores the temporal dynamics of wildfire occurrences, confirming their dependence on various environmental variables, including the maximum daily temperature, wind speed, surface pressure, and total precipitation.

stat.AP↗

arXiv2023

Advances in Kth nearest-neighbour clutter removal

We consider the problem of feature detection in the presence of clutter in spatial point processes. Classification methods have been developed in previous studies. Among these, Byers and Raftery (1998) models the observed Kth nearest neighbour distances as a mixture distribution and classifies the clutter and feature points consequently. In this paper, we enhance such approach in two manners. First, we propose an automatic procedure for selecting the number of nearest neighbours to consider in the classification method by means of segmented regression models. Secondly, with the aim of applying the procedure multiple times to get a ``better" end result, we propose a stopping criterion that minimizes the overall entropy measure of cluster separation between clutter and feature points. The proposed procedures are suitable for a feature with clutter as two superimposed Poisson processes on any space, including linear networks. We present simulations and two case studies of environmental data to illustrate the method.

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arXiv2023

Feature detection in point processes on linear networks using nearest neighbour volumes

We consider the feature detection problem in the presence of clutter in point processes on linear networks. We extend the classification method developed in previous studies to this more complex geometric context, where the classical properties of a point process change and data visualization are not intuitive. We use the K-th nearest neighbour volumes distribution in linear networks for this approach. As a result, our method is suitable for analysing point patterns consisting of features and clutter as two superimposed Poisson processes on the same linear network. To illustrate the method, we present simulations and examples of road traffic accidents that resulted in injuries or deaths in two cities in Colombia.

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arXiv2023

stopp: Methods for spatio-temporal point pattern analysis, simulation, model fitting, diagnostics, and local analyses

The stopp R package deals with spatio-temporal point processes which might have occurred on the Euclidean space or on some specific linear networks such as roads of a city. The package contains functions to summarize, plot, and perform different kinds of analyses on point processes, mainly following the methods proposed in some recent papers in the stream of scientific literature. The main topics of such works, and of the package in turn, include modeling, statistical inference, and simulation issues on spatio-temporal point processes on Euclidean space and linear networks, with a focus on their local characteristics. We contribute to the existing literature by collecting many of the most widespread methods for the analysis of spatio-temporal point processes into a unique package, which is intended to welcome many further proposals and extensions.

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arXiv2022

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

We propose a local version of spatio-temporal log-Gaussian Cox processes using 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 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. We present simulation studies to assess the performance of the proposed fitting procedure, and show an application to seismic spatio-temporal point pattern data.

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arXiv2022

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 simulation study we show that the test is able to detect local deviations from random labelling. We also provide an application to an earthquake point pattern with functional marks given by seismic waveforms.

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arXiv2020

Spatial Bayesian Hierarchical Modelling with Integrated Nested Laplace Approximation

We consider latent Gaussian fields for modelling spatial dependence in the context of both spatial point patterns and areal data, providing two different applications. The inhomogeneous Log-Gaussian Cox Process model is specified to describe a seismic sequence occurred in Greece, resorting to the Stochastic Partial Differential Equations. The Besag-York-Mollie model is fitted for disease mapping of the Covid-19 infection in the North of Italy. These models both belong to the class of Bayesian hierarchical models with latent Gaussian fields whose posterior is not available in closed form. Therefore, the inference is performed with the Integrated Nested Laplace Approximation, which provides accurate and relatively fast analytical approximations to the posterior quantities of interest.

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