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The algorithms used for the optimal management of an ambulance fleet require an accurate description of the spatiotemporal evolution of the emergency events. In the last years, several authors have proposed sophisticated statistical approaches to forecast ambulance dispatches, typically modelling the data as a point pattern occurring on a planar region. Nevertheless, ambulance interventions can be more appropriately modelled as a realisation of a point process occurring on a linear network. The constrained spatial domain raises specific challenges and unique methodological problems that cannot be ignored when developing a proper statistical approach. Hence, this paper proposes a spatiotemporal model to analyse ambulance dispatches focusing on the interventions that occurred in the road network of Milan (Italy) from 2015 to 2017. We adopt a nonseparable first-order intensity function with spatial and temporal terms. The temporal dimension is estimated semiparametrically using a Poisson regression model, while the spatial dimension is estimated nonparametrically using a network kernel function. A set of weights is included in the spatial term to capture space-time interactions, inducing nonseparability in the intensity function. A series of tests show that our approach successfully models the ambulance interventions and captures the space-time patterns more accurately than planar or separable point process models.

The Hodrick-Prescott filter is a popular macroeconomics tool to decompose time series into a smooth trend and a business cycle components. The last few years have witnessed global events, such as the Global Financial Crisis, the COVID-19 pandemic, and the war in Ukraine, that have had abrupt structural impacts on many economic time series. At the same time, governments in Western countries have been arranging structural reforms to adapt their labor markets to socio-economic changes. Among the countries at the center of these processes stands Italy. Accordingly, it is reasonable to assume that the combination of structural reforms and socioeconomic shocks have generated structural changes in the number of employed people within the country. We then employ a robust version of the Hodrick-Prescott filter to identify structural breaks in the quarterly time series of employed people in Italy for different age groups from 1993 to 2023.

To analyze the environmental and economic impact of the ammonia (NH3) emissions a state-space area level model to handle data of the Italian Lombard agrarian subregions is presented. The extended version of the Fay-Herriot model is needed to improve the design-based official statistics estimates.

The cluster-weighted model (CWM) is a member of the family of mixture of regression models and is also known as mixtures of regressions with random covariates. CWMs refer to the framework of model-based clustering and have their natural application when the research interest requires modeling the relationship between a response variable and a set of covariates using a regression-based approach such as a generalized linear model and the sample is suspected to be composed by heterogeneous latent classes. Software for estimating these models is not yet available in Stata. The aim of this article is to introduce the Stata package \code{cwmglm}, which allows fitting CWMs based on the most common generalized linear models with random covariates. Moreover, \code{cwmglm} allows the estimation of parsimonious models of Gaussian distributions, with the parametrization of the variance-covariance matrix based on the eigenvalue decomposition. These features are completely new for Stata users. The \code{cwmglm} package features goodness-of-fit, bootstrapping and model selection tools. We illustrate the use of \code{cwmglm} with real and simulated datasets

Species-sampling problems (SSPs) refer to a vast class of statistical problems calling for the estimation of (discrete) functionals of the unknown species composition of an unobservable population. A common feature of SSPs is their invariance with respect to species labeling, which is at the core of the Bayesian nonparametric (BNP) approach to SSPs under the popular Pitman-Yor process (PYP) prior. In this paper, we develop a BNP approach to SSPs that are not “invariant” to species labeling, in the sense that an ordering or ranking is assigned to species’ labels. Inspired by the population genetics literature on age-ordered alleles’ compositions, we study the following SSP with ordering: given an observable sample from an unknown population of individuals belonging to species (alleles), with species’ labels being ordered according to weights (ages), estimate the frequencies of the first r order species’ labels in an enlarged sample obtained by including additional unobservable samples. By relying on an ordered PYP prior, we obtain an explicit posterior distribution of the first r order frequencies, with estimates being of easy implementation and computationally efficient. We apply our approach to the analysis of genetic variation, showing its effectiveness in estimating the frequency of the oldest allele, and then we discuss other potential applications.

The adage “the rich are getting richer” refers to increasingly skewed and heavily-tailed income distributions. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are mean based. In view of this, it has been proposed in the literature to incorporate the median into the definition of the Gini index. In the present paper we make a further step in this direction and, to acknowledge the possibility of differing viewpoints, investigate three median-based indices of inequality. These indices overcome past limitations, such as: (1) they do not rely on the mean as the center of, or a reference point for, income distributions, which are skewed, and are getting even more heavily skewed; (2) they are suitable for populations of any degree of tail heaviness, and income distributions are becoming increasingly such; and (3) they are unchanged by, and even discourage, transfers among the rich persons, but they encourage transfers from the rich to the poor, as well as among the poor to alleviate their hardship. We study these indices analytically and numerically using various income distribution models. Real-world applications are showcased using capital incomes from 2001 and 2018 surveys from fifteen European countries.

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions for the emergence of some form of almost sure asymptotic synchronization. Specifically, we identify three regimes: the first involves complete synchronization, where all processes converge towards the same random variable; the second exhibits almost sure convergence of the system, but no form of synchronization subsists; and the third reveals a scenario where there is almost sure asymptotic synchronization within the cyclic classes of the interaction matrix, together with an asymptotic periodic behavior among these classes.

Cluster-weighted models (CWMs) are an important class of machine learning models that are commonly used for modelling complex datasets. However, they are known to suffer from reduced computing efficiency and estimator accuracy when dealing with high-dimensional data. Previous work has proposed a parsimonious technique that can improve CWMs’ performance in the high-dimensional data paradigm. However, this method has a setback for very high-dimensional data, where the dimensionality is greater than 100. In this paper, we propose a new hybridised method that incorporates a dimensionality reduction technique called T-distributed stochastic neighbour embedding (TSNE) to enhance the parsimonious CWMs in high-dimensional space. Additionally, we introduce a novel heuristic for detecting the hidden components of the underlying mixture model, which can be used with the popular R package FlexCWM. We evaluated the performance of the proposed method using two real datasets and found that it improves clustering power when compared to both the parsimony methods and the TSNE methods combined with CWMs in the high-dimensional data setting. Our results suggest that the proposed method can improve the efficiency and accuracy of CWMs in dealing with high-dimensional data, making it a valuable tool for data scientists and statisticians.

We implement an analytic approach for ordinal measures and we use it to investigate the structure and the changes over time of self-worth in a sample of adolescents students in high school. We represent the variations in self-worth and its various sub-domains using entropy-based measures that capture the observed uncertainty. We then study the evolution of the entropy across four time points throughout a semester of high school. Our analytic approach yields information about the configuration of the various dimensions of the self together with time-related changes and associations among these dimensions. We represent the results using a network that depicts self-worth changes over time. This approach also identifies groups of adolescent students who show different patterns of associations, thus emphasizing the need to consider heterogeneity in the data.

Traditional sampling methods may prove inadequate when dealing with spatially clustered populations or when studying rare events or traits that are not easily detectable across the target population. When both scenarios occur simultaneously, adaptive sampling strategies can represent a viable option to enhance the detectability of cases of interest. This paper delves into the application of a novel class of sequential adaptive sampling strategies to animal surveys. These strategies, originally proposed for human population tuberculosis prevalence surveys, allow oversampling of the rare interest variables while managing on-field constraints. This ensures that the unfixed sample size, typical of adaptive sampling, does not compromise overall cost-effectiveness. We explore a strategy within this class that integrates an adaptive component into a Poisson sequential selection. The aim is twofold: to intensify the detection of cases by exploiting the spatial clustering and to provide a flexible framework for managing logistics and budget constraints. To illustrate the strengths and weaknesses of this Poisson-based sequential adaptive sampling strategy compared to traditional sampling methods, a simulation study was conducted on a blue-winged teal population in Florida, USA. The results showcase the benefits of the proposed strategy and open avenues for future methodological and practical improvements.

Building Performance Simulation extensively uses statistical learning techniques for quicker insights and improved accessibility. These techniques help understand the relationship between input variables and the desired outputs, and they can predict unknown observations. Prediction becomes more informative with uncertainty quantification, which involves computing prediction intervals. Conformal prediction has emerged over the past 25 years as a flexible and rigorous method for estimating uncertainty. This approach can be applied to any pre-trained model, creating statistically rigorous uncertainty sets or intervals for model predictions. This study uses data from simulated buildings to demonstrate the powerful applications of conformal prediction in Building Performance Simulation (BPS) and, consequently, to the broader energy sector. Results show that conformal prediction can be applied when any assumptions about input and output variables are made, enhancing understanding and facilitating informed decision-making in energy system design and operation.

This paper proposes comparative research on support provided outside the household by older adults in Europe. In studying social support, the network perspective is widely used, investigating, in particular, the ego-centered support networks of individuals. The analysis is based on data from Wave 7 of the Survey of Health Ageing and Retirement in Europe (SHARE). It examines the characteristics of ego-support networks of individuals aged 65 and over in 12 European countries, which are grouped into a novel welfare regime typology. Through Multiple Correspondence Analysis, we jointly looked into the categorical variables describing the recipients (alters) of the support provided by older adults and the welfare regime classification. As a main result, countries grouped in “High degree of familialism by default” category specialized in supporting family-related alters, particularly with childcare or personal care. In contrast, the elders in countries belonging to “High degree of de-familialisation” typology provided a more varied but less demanding support, to non-relatives alters and less oriented to care. The analyses show that the SHARE provides a solid opportunity to face the topic.

We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.

In questa tesi, adottiamo il setting di modelli di mistura bayesiani, sfruttando la loro flessibilità e adattabilità per affrontare una serie di domande di ricerca che sono challenging e che riguardano il clustering dei dati. Questo manoscritto è una raccolta di tre progetti. I primi due progetti sono dedicati all'utilizzo dei metodi bayesiani non parametrici (BNP). Nel progetto conclusivo, ci concentriamo su un contesto parametrico e forniamo un nuovo quadro metodologico per indagare specifiche domande di ricerca che emergono nell’area del topic modelling. Il manoscritto affronta domande di ricerca distinte, ciascuna affrontata attraverso la lente della metodologia bayesiana. Nel Capitolo 2 affrontiamo la sfida del clustering simultaneo di utenti ed items all'interno di dataset contenenti informazioni mancanti, come spesso accade da dati provenienti dalle piattaforme social. Proponiamo un metodo innovativo di co-clustering che consente di avere censura informativa, fornendo una soluzione solida per la gestione dei dati mancanti e l'estrazione di informazioni dai dati. Il Capitolo 3 sposta l'attenzione verso la modellazione dell'evoluzione delle partizioni dei dati nel tempo, esplorando il rilevamento dinamico di changepoint utilizzando random partition model. Questo approccio cattura l'evoluzione delle strutture di partizione rilevando al tempo stesso in modo efficace i changepoint, contribuendo in modo significativo al campo dei modelli per partizioni con dipendenza temporale. Nel capitolo finale, introduciamo un nuovo modello basato su distribuzioni definite sul simplesso per affrontare il problema se tali distribuzioni possano catturare varie forme di dipendenza tra argomenti in un corpus di documenti testuali. La nostra indagine ci porta alla definizione di un modello caratterizzato da correlazione positiva tra topic, evidenziando la versatilità e l'applicabilità delle distribuzioni basate sul simplesso nel modellare relazioni complesse all'interno di set, Throughout this thesis, we embrace the Bayesian mixture models setting, harnessing their flexibility and adaptability to address a range of challenging research questions concerning data clustering. This manuscript is a collection of three projects. The first two projects are dedicated to the use of Bayesian Nonparametric (BNP) methods. In the concluding project, we focus on a parametric setting, and provide a novel methodological framework to investigate specific research inquiries arising in topic modeling. The manuscript addresses distinct research questions, each approached through the lens of Bayesian methodology. In Chapter 2, we tackle the challenge of simultaneous clustering of users and items within datasets riddled with missing information, a common occurrence in data from social platforms. We propose an innovative co-clustering method that accommodates informative censoring, providing a robust solution for handling missing data and extracting valuable insights. Chapter 3 shifts the focus towards modeling the evolution of data partitions over time, exploring dynamic changepoint detection using temporal random partition models. This approach captures evolving partition structures while effectively detecting changepoints, contributing significantly to the field of temporal modeling with random partitions. In the final chapter, we introduce a novel model based on distributions defined on the simplex to address the intriguing question of whether such distributions can capture various forms of dependence among topics in a corpus of textual documents. Our investigation leads us to the definition of a model characterized by positive correlation across topics, highlighting the versatility and applicability of simplex-based distributions in modeling complicated relationships within textual datasets. In summary, this thesis aims at providing a thoughtful perspective on Bayesian mixture models and their applications, while also presenting innovative solutions to vari

In generale, nella ricerca sull'identificazione degli argomenti, è sempre difficile trovare un set di dati di addestramento di alta qualità con una miscela nota di argomenti per ciascun testo e in modo che gli argomenti provengano da una tassonomia che copra tutti i possibili argomenti. Un dataset di questo tipo, preferibilmente esteso e facilmente aggiornabile, sarebbe di enorme valore per addestrare modelli supervisionati o per validare i risultati di vari tipi di modelli. Inoltre, i TM hanno dimostrato di essere altamente efficaci in numerosi test dall’introduzione del modello Latent Dirichlet Allocation (LDA). Sebbene negli ultimi anni siano state sviluppate molte varianti e evoluzioni, tutti affrontano due problemi. In primo luogo, è difficile comprendere quale sia il “significato” degli argomenti latenti identificati. Per risolvere questo problema, sono stati proposti diversi metodi per etichettare questi argomenti latenti. In secondo luogo, confrontare diversi TM è complicato perché non esiste una relazione diretta tra gli argomenti di un modello e quelli di un altro. Di conseguenza oggi possiamo contare solo su indicatori “autoreferenziali” o su verifiche manuali. In questa ricerca di dottorato vengono proposte molte nuove metodologie su queste tre sfide: due metodologie per creare un ampio corpus di documenti con un mix ben definito di argomenti, quattro metodi per etichettare argomenti latenti utilizzando questo corpus con un approccio supervisionato, sei metriche utilizzate per la valutazione delle prestazioni dei modelli tematici in questo contesto. Questi tre apporti significativi consentono di ottenere il contributo principale di questa ricerca: stabilire un quadro metodologico rigoroso per confrontare diversi TM su un’”arena” comune e oggettiva, fornendo l’opportunità di confronti quantitativi delle prestazioni, in particolare sulla loro capacità di identificare accuratamente i mix effettivo di argomenti reali nei documenti. Sono stati condotti, One common task in Natural Language Processing (NLP) is topics identification, which involves recognizing the topic(s) of a text. Among the automatic solutions (in contrast to engines developed and maintained by linguistic experts), there are two main approaches: Statistical Learning Models (SLM) trained on supervised datasets, capable of identifying real topics and Topic Models (TM), capable of identifying latent topics in unsupervised corpora of documents. In general, in topic identification research, it is always challenging to find a high-quality training dataset with a known mixture of topics for each text and so that topics come from a taxonomy that covers all possible subjects. A dataset of this kind, preferably extensive and easy updatable, could be of enormous value to train supervised models or to validate the results of various types of models. Furthermore, TMs have proven to be highly effective in numerous tests since the introduction of the Latent Dirichlet Allocation (LDA) model. While many variants and advancements have been developed in recent years, they all face two issues. Firstly, it is difficult to comprehend what are the ”meaning” the identified latent topics. To address this, several methods for labeling these latent topics have been proposed. Secondly, comparing different TMs is tricky because there is no direct relationship between the topics of one model and those of another. Consequently today we have only been able to rely on ”self-referential” indicators or manual verification. In this PhD research many novel methodologies are proposed on these three challenges: two methodologies for creating a large corpus of documents with well-defined mix of topics, four methods for labeling latent topics using this corpus with a supervised approach, six metrics used for performances evaluation of topic models in this context. These three significant advancements allows to get the main contribution of this research: to establish a rigorous methodologi

La nozione di intervento esterno è di fondamentale importanza negli ambiti dell'inferenza causale e della scoperta causale da combinazioni di dati osservazionali e sperimentali. Nel primo, essa costituisce uno strumento fondamentale per la definizione, identificazione e stima degli effetti causali. Nel secondo, consente di definire precisamente ciò che i dati sperimentali implicano, consentendo così il loro utilizzo per migliorare l'identificabilità delle strutture causali da stimare. Questa tesi affronta entrambi gli ambiti attraverso la lente dell'inferenza bayesiana. Il manoscritto è composto da tre capitoli, di cui il primo serve da introduzione all'ambito generale della tesi, delineandone il contesto scientifico e il contributo. I principali due capitoli scaturiscono da due progetti indipendenti, ma accomunati dall'idea di estendere la nozione di intervento esterno al fine di riflettere gli esperimenti realmente condotti nell'attività di ricerca scientifica. Nel Capitolo 2, consideriamo il caso di interventi congiunti che coinvolgono più variabili simultaneamente. In particolare, proponiamo un approccio bayesiano che, nel contesto gaussiano, unisce le metodologie di scoperta causale a quelle di stima degli effetti causali, risultando in una metodologia di Bayesian model averaging per la stima di effetti causali congiunti quando la struttura causale del processo generatore dei dati è ignota. Nel Capitolo 3, analizziamo interventi che modificando il meccanismo causale delle variabili target e che chiamiamo general interventions. In tale contesto, costruiamo una metodologia bayesiana di scoperta causale da combinazioni di dati osservazionali e sperimentali, ipotizzando che questi ultimi abbiano la loro origine in general intervention con target ignote. Inoltre, definiamo e diamo una caratterizzazione grafica del limite di identificabilità delle strutture causali e disegniamo un algoritmo MCMC per campionare dalla distribuzione a posteriori congiunta sullo, The notion of external intervention is of fundamental importance within the fields of causal inference and causal discovery from combinations of observational and experimental data. In the former, it serves as a tool for defining, identifying, and estimating causal effects. In the latter, it allows for a precise definition of what experimental data entail, enabling their usage to improve the identifiability of causal structures. This thesis addresses both aspects, investigating them within the Bayesian framework. The manuscript comprises three chapters, with the first serving as an introduction to the general scope of the thesis, outlining its scientific context and contribution. The main two chapters represent two independent projects, both driven by the objective of broadening the notion of external intervention to reflect the diverse manipulations that scientists may actually implement in their experiments. In Chapter 2, we consider the case of joint interventions which may simultaneously affect several variables. In particular, we present a unified Bayesian approach for causal discovery and causal effect estimation in the Gaussian setting. This leads to a Bayesian model averaging strategy for estimating the joint causal effects associated with such interventions when the causal structure of the data-generating process is unknown. In Chapter 3, we instead consider interventions modifying the causal mechanisms of the intervened variables, which we call general interventions. We thus construct a Bayesian model for causal discovery from combinations of observational and experimental data originating from unknown general interventions. In addition, we provide definitions and graphical characterizations of the identifiability limit of causal structures in the new setting and devise a suitable MCMC scheme to sample from the joint posterior distribution over causal structures and unknown general interventions.

We propose a multivariate regime switching model based on a Student- (Formula presented.) copula function with parameters controlling the strength of correlation between variables and that are governed by a latent Markov process. To estimate model parameters by maximum likelihood, we consider a two-step procedure carried out through the Expectation–Maximisation algorithm. To address the main computational burden related to the estimation of the matrix of dependence parameters and the number of degrees of freedom of the Student- (Formula presented.) copula, we show a novel use of the Lagrange multipliers, which simplifies the estimation process. The simulation study shows that the estimators have good finite sample properties and the estimation procedure is computationally efficient. An application concerning log-returns of five cryptocurrencies shows that the model permits identifying bull and bear market periods based on the intensity of the correlations between crypto assets.

We propose a variable selection method for multivariate hidden Markov models with continuous responses that are partially or completely missing at a given time occasion. Through this procedure, we achieve a dimensionality reduction by selecting the subset of the most informative responses for clustering individuals and simultaneously choosing the optimal number of these clusters corresponding to latent states. The approach is based on comparing different model specifications in terms of the subset of responses assumed to be dependent on the latent states, and it relies on a greedy search algorithm based on the Bayesian information criterion seen as an approximation of the Bayes factor. A suitable expectation-maximization algorithm is employed to obtain maximum likelihood estimates of the model parameters under the missing-at-random assumption. The proposal is illustrated via Monte Carlo simulation and an application where development indicators collected over eighteen years are selected, and countries are clustered into groups to evaluate their growth over time.

The COVID-19 pandemic caused an unprecedented excess mortality. Since 2020, many studies have focussed on the characteristics of COVID-19 patients who did not survive. From the statistical point of view, what seems to dominate is the large heterogeneity of the populations affected by COVID-19 and the extreme difficulty in identifying subpopulations who died affected by a plurality of contemporary characteristics. In this paper, we propose an extremely flexible approach based on a cluster-weighted model, which allows us to identify latent groups of patients sharing similar characteristics at the moment of hospitalisation as well as a similar mortality. We focus on one of the hardest hit areas in Italy and study the heterogeneity in the population of patients affected by COVID-19 using administrative data on hospitalisations in the first wave of the pandemic. Results highlighted that a model-based clustering approach is essential to understand the complexity of the COVID-19 patients treated by hospitals and who die during hospitalisation.

In this paper, we propose a new class of assortativity measures for weighted and directed networks. We extend Newman's classical degree–degree assortativity by considering node attributes other than degree, and we propose connections among nodes via directed walks of length greater than one, thus obtaining higher-order assortativity. We test the new measure in the paradigmatic case of the world trade network and for other networks from a socioeconomic context, and we also provide some simulation results. Importantly, we show how this global network indicator is strongly related to the autocorrelations of the states of a Markov chain.

We present ARPALData, an R package that can help international users retrieve, handle, and analyze air quality and weather data in the Lombardy region (Northern Italy). The software provides a user-friendly tool that directly inquires into the platform of the regional environmental protection agency and ensures real-time updating of information using standardized syntax. The software provides data in standard statistical formats. Eventually, all measurements, metadata, and subsequent analytical tools are provided to users in English, facilitating accessibility to international and domestic users. Data are collected from the open database of the Regional Agency for Environmental Protection of Lombardy, namely ARPA Lombardia. ARPALData returns measurements at several temporal frequencies (infra-hourly to yearly) collected through air quality and weather ground monitoring networks managed by ARPA Lombardia, as well as estimates of several pollutants at the municipal level. In addition to data download functions, ARPALData provides functions to explore, describe, analyze, and graphically represent air quality and weather data. In particular, users are provided with functions to compute key descriptive statistics and input data maps, temporally aggregate measurements, detect outliers, and study missing-value (gap length) patterns. Herein, we discuss purposes, goals, and functioning of the package, and present three guided examples and case studies in which the software is used to characterize air quality and meteorology in different settings. The examples are designed to provide a step-by-step guide for accomplished analyses using the most relevant tools included in ARPALData.

We examine the effect of streaming based on ability levels on individuals’ civic participation throughout their adult life. The hypothesis we test is that ability grouping influences individuals’ general self-concept and, consequently, their civic participation choices across the life course. We employ data from the British National Child Development Study, which follows all UK citizens born during a certain week in 1958. Six binary variables observed at 33, 42, and 51 years of age are considered to measure civic participation. Our approach defines causal estimands with multiple treatments referring to the evolution of civic engagement over time in terms of potential versions of a sequence of latent variables assumed to follow a Markov chain with initial and transition probabilities depending on posttreatment time-varying covariates. The model also addresses partially or entirely missing data on one or more indicators at a given time occasion and missing posttreatment covariate values using dummy indicators. The model is estimated by maximizing a weighted log-likelihood function with weights corresponding to the inverse probability of the received treatment obtained from a multinomial logit model based on pretreatment covariates. Our results show that ability grouping affects the civic participation of high-ability individuals when they are 33 years old with respect to participation in general elections.

This study presents a comparative analysis of three predictive models with an increasing degree of flexibility: hidden dynamic geostatistical models (HDGM), generalised additive mixed models (GAMM), and the random forest spatiotemporal kriging models (RFSTK). These models are evaluated for their effectiveness in predicting PM 2.5 concentrations in Lombardy (North Italy) from 2016 to 2020. Despite differing methodologies, all models demonstrate proficient capture of spatiotemporal patterns within air pollution data with similar out-of-sample performance. Furthermore, the study delves into station-specific analyses, revealing variable model performance contingent on localised conditions. Model interpretation, facilitated by parametric coefficient analysis and partial dependence plots, unveils consistent associations between predictor variables and PM 2.5 concentrations. Despite nuanced variations in modelling spatiotemporal correlations, all models effectively accounted for the underlying dependence. In summary, this study underscores the efficacy of conventional techniques in modelling correlated spatiotemporal data, concurrently highlighting the complementary potential of Machine Learning and classical statistical approaches.

I modelli statistici per serie storiche multivariate sono strumenti utili per comprendere e prevedere le interazioni tra diverse variabili. Le tecniche di clustering temporale aiutano ulteriormente nell'analisi di tali dati, identificando insiemi di serie storiche con tendenze simili nel tempo. Tuttavia, una modellazione accurata è essenziale per migliorare l'accuratezza delle previsioni e la rilevazione delle anomalie. Le serie storiche finanziarie presentano sfide uniche dovute alle loro caratteristiche, come il volatility clustering, le code pesanti, la non linearità e la non normalità. Inoltre, possono sorgere sfide computazionali a causa dell'alta dimensionalità di tali dati. In questa tesi, vengono proposte due metodologie chiave per la modellazione e il clustering di serie storiche finanziarie multivariate. Nel Capitolo 2, si introduce il modello regime switching copula Student-t, un potente strumento per catturare la distribuzione con code pesanti dei rendimenti finanziari in diverse condizioni di mercato. Questo modello combina la flessibilità della distribuzione della copula Student-t con la capacità di cambiare tra stati del mercato. Si propone un nuovo approccio di stima basato su massima verosimiglianza, affrontando le sfide computazionali legate alla stima di tali modelli per dati multivariati. La proposta viene testata attraverso uno studio di simulazione, dimostrando che essa fornisce buoni risultati su campioni finiti. L'approccio proposto viene in seguito applicato per modellare la distribuzione congiunta dei log-rendimenti delle cinque principali criptovalute, dimostrandone l'efficacia nel tracciare le fasi di mercato rialzista e ribassista. Nel Capitolo 3 viene presentato il modello sparse statistical jump, progettato per affrontare le sfide dei dati finanziari ad alta dimensionalità. Esso consente di identificare le variabili chiave all'interno di un insieme ad alta dimensionalità, modellando contemporaneamente la sequenza di stati laten, Multivariate time series models are useful tools for understanding and predicting the interactions among multiple variables. Temporal clustering techniques further aid in analyzing such data by identifying sets of time series that exhibit similar trends over time. However, accurate modeling and clustering are essential for enhancing forecasting accuracy and anomaly detection. Financial time series data present unique challenges due to their characteristics such as volatility clustering, heavy tails, non-linearity, and non-normality. Moreover, computational challenges can arise due to the high-dimensionality of such data. In this thesis, we propose two key methodologies for modeling and clustering multivariate financial time series data, taking into account their characteristics. In Chapter 2, we first introduce the regime switching Student-t copula model, a powerful tool for capturing the heavy-tailed joint distribution of financial returns across different market conditions. This model combines the flexibility of the Student-t copula distribution with the ability to switch between market states. We propose a novel maximum likelihood estimation approach tailored for this model, addressing computational challenges associated with estimating copula models for multivariate data. We test the proposal through an extensive simulation study and we show that it provides good results in finite samples. We apply our approach to model the joint distribution of the five main cryptocurrency log-returns, demonstrating its effectiveness in tracking bull and bear market phases based on cryptocurrency correlations. In Chapter 3, we present the sparse statistical jump model, designed to address the challenges of high-dimensional financial data. This model allows for the identification of key drivers within a high dimensional set of candidate variables while modeling the hidden state sequence. The sparse statistical jump model is particularly advantageous, as it allows for simultaneou

Spatial data are becoming increasingly accessible to urban scientists, but these data are often prone to measurement error. Motivated by the analysis of the Milan (Italy) apartment market heterogeneity, we propose a semiparametric approach to adjust for the presence of measurement error in the covariates when estimating M-quantile regression. The M-quantile approach helps explain the heterogeneity across individual units, preserving robustness and efficiency in the estimates. The model’s parameters are estimated within a penalised likelihood framework and an analytical expression is proposed to estimate standard errors. Asymptotic properties of estimates are also provided.

We propose a twofold adjustment for Event Studies considering spatiotemporal data in a multivariate time series framework where the data are characterized by spatial and temporal dependence. The first adjustment consists of modeling the spatiotemporal dynamics of the data by implementing several geostatistical models capable of handling both spatial and temporal components, as well as estimating the relationship between the response variable and a set of exogenous factors. With the second adjustment, we propose to use cross-sectional-adjusted test statistics directly accounting for spatial cross-correlation. The proposed methods are applied to the case of NO 2 concentrations observed in Northern Italy during the first wave of the COVID-19 pandemic. The key findings are as follows. First, all the considered geostatistical models estimate larger reductions in the major metropolitan and congested areas, while smaller reductions are estimated in rural plains and in the mountains. Second, the models are nearly equivalent in terms of fitting and are capable of identifying the true event window. Third, by using spatiotemporal models we ensure the residuals are uncorrelated across space and time, thus allowing Event Studies test statistics to provide reliable and realistic estimates. Fourth, as expected, all test statistics show significant reductions in NO 2 concentrations starting from the first few days of lockdown. Supplementary materials accompanying this paper appear online.

Gibbs-type priors are combinatorial processes widely used as key components in several Bayesian nonparametric models. By virtue of their flexibility and mathematical tractability, they turn out to be predominant priors in species sampling problems and mixture modeling. We introduce a new family of processes which extends the Gibbs-type one, by including a contaminant component in the model to account for an excess of observations with frequency one. We first investigate the induced random partition, the associated predictive distribution, the asymptotic behavior of the total number of blocks and the number of blocks with a given frequency: all the results we obtain are in closed form and easily interpretable. A remarkable aspect of contaminated Gibbs-type priors relies on their predictive structure, compared to the one of the standard Gibbs-type family: it depends on the additional sampling information on the number of observations with frequency one out of the observed sample. As a noteworthy example we focus on the contaminated version of the Pitman-Yor process, which turns out to be analytically tractable and computationally feasible. Finally we pinpoint the advantage of our construction in different applications: we show how it helps to improve predictive inference in a species-related dataset exhibiting a high number of species with frequency one; we also discuss the use of the proposed construction in mixture models to perform density estimation and outlier detection.

Compositional data are vectors typically representing proportions of a whole, that is, those whose elements are strictly positive and subject to a unit-sum constraint. The increasing number of fields where this type of data arises makes the development of proper statistical tools an important issue. From a regression perspective, whenever the multivariate response is a compositional vector, a proper model that accounts for the unit-sum constraint is the well-established Dirichlet regression model. However, there are significant drawbacks mainly due to the limited flexibility of the Dirichlet distribution. The aim of this contribution is to introduce a new multivariate regression model for constrained responses, that is based on the extended flexible Dirichlet distribution (which is a structured mixture with Dirichlet distributed components). The new model is obtained by adopting a novel reparameterization which allows for, among other things, the presence of suitably designed cluster-specific regression patterns. It is shown to provide considerably greater flexibility and better performance than the standard Dirichlet regression model. In particular, from theoretical analysis, intensive simulation studies in many challenging scenarios, as well as from a real data application, it emerges that the new regression model can handle several issues affecting the Dirichlet regression, such as the presence of outliers, latent groups, multi-modality, and positive correlations.

This paper proposes an M-quantile regression approach to address the heterogeneity of the housing market in a modern European city. We show how M-quantile modelling is a rich and flexible tool for empirical market price data analysis, allowing us to obtain a robust estimation of the hedonic price function whilst accounting for different sources of heterogeneity in market prices. The suggested methodology can generally be used to analyse nonlinear interactions between prices and predictors. In particular, we develop a spatial semiparametric M-quantile model to capture both the potential nonlinear effects of the cultural environment on pricing and spatial trends. In both cases, nonlinearity is introduced into the model using appropriate bases functions. We show how the implicit price associated with the variable that measures cultural amenities can be determined in this semiparametric framework. Our findings show that the effect of several housing attributes and urban amenities differs significantly across the response distribution, suggesting that buyers of lower-priced properties behave differently than buyers of higher-priced properties.

There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in Bayesian nonparametric (BNP) inference for the unseen-features problem: for fixed prior’s parameters, they all lead to a Poisson posterior distribution for the number of unseen features, which depends on the sampling information only through the sample size. CRMs are thus not a flexible prior model for the unseen-features problem and, while the Poisson posterior distribution may be appealing for analytical tractability and ease of interpretability, its independence from the sampling information makes the BNP approach a questionable oversimplification, with posterior inferences being completely determined by the estimation of unknown prior’s parameters. In this article, we introduce the stable-Beta scaled process (SB-SP) prior, and we show that it allows to enrich the posterior distribution of the number of unseen features arising under CRM priors, while maintaining its analytical tractability and interpretability. That is, the SB-SP prior leads to a negative Binomial posterior distribution, which depends on the sampling information through the sample size and the number of distinct features, with corresponding estimates being simple, linear in the sampling information and computationally efficient. We apply our BNP approach to synthetic data and to real cancer genomic data, showing that: (i) it outperforms the most popular parametric and nonparametric competitors in terms of estimation accuracy; (ii) it provides improved coverage for the estimation with respect to a BNP approach under CRM priors. Supplementary materials for this article are available online.

Traditionally, common testing problems are formalized in terms of a precise null hypothesis representing an idealized situation such as absence of a certain “treatment effect”. However, in most applications the real purpose of the analysis is to assess evidence in favor of a practically relevant effect, rather than simply determining its presence/absence. This discrepancy leads to erroneous inferential conclusions, especially in case of moderate or large sample size. In particular, statistical significance, as commonly evaluated on the basis of a precise hypothesis low p value, bears little or no information on practical significance. This paper presents an innovative approach to the problem of testing the practical relevance of effects. This relies upon the proposal of a general method for modifying standard tests by making them suitable to deal with appropriate interval null hypotheses containing all practically irrelevant effect sizes. In addition, when it is difficult to specify exactly which effect sizes are irrelevant we provide the researcher with a benchmark value. Acceptance/rejection can be established purely by deciding on the (ir)relevance of this value. We illustrate our proposal in the context of many important testing setups, and we apply the proposed methods to two case studies in clinical medicine. First, we consider data on the evaluation of systolic blood pressure in a sample of adult participants at risk for nutritional deficit. Second, we focus on a study of the effects of remdesivir on patients hospitalized with COVID-19.

In a network of reinforced stochastic processes, for certain values of the parameters, all the agents' inclinations synchronize and converge almost surely toward a certain random variable. The present work aims at clarifying when the agents can asymptotically polarize, i.e. when the common limit inclination can take the extreme values, 0 or 1, with probability zero, strictly positive, or equal to one. Moreover, we present a suitable technique to estimate this probability that, along with the theoretical results, has been framed in the more general setting of a class of martingales taking values in [0, 1] and following a specific dynamics.

Il rischio operativo (OpRisk) emerge come una tematica non finanziaria fondamentale con implicazioni di vasta portata per le istituzioni finanziarie. Allontanandosi dai compiti normativi convenzionali che comprendono la raccolta dei dati, il calcolo dei requisiti patrimoniali e la generazione di report per le decisioni manageriali, le funzioni di OpRisk stanno ora perseguendo attivamente strategie proattive per prevenire o alleviare gli impatti del rischio. Ad esempio, le tecniche di intelligenza artificiale, sempre più importanti per gli insight manageriali, vengono ora impiegate per estrarre informazioni aggiuntive dai dati. Questo studio prevede l'applicazione delle tecniche di analisi del testo, un elemento fondamentale dell'elaborazione del linguaggio naturale, alle descrizioni degli eventi OpRisk. Il presente lavoro introduce un flusso strutturato per l'applicazione di tecniche di analisi del testo alle descrizioni degli eventi OpRisk per identificare cluster gestionali (più granulari rispetto alle categorie normative) che rappresentano le cause principali degli OpRisk sottostanti. Tuttavia, questi potenti approcci presentano limitazioni nell’influenzare l’impatto di futuri eventi di perdita. Come risposta, questa ricerca approfondisce l’integrazione delle fonti di dati tradizionali, esplorando canali alternativi per identificare potenziali eventi nelle loro prime fasi e gestirne in modo proattivo l’impatto. Un aspetto innovativo prevede l’analisi dei tweet rilevanti di X (ex Twitter) per la scansione continua del contesto di rischio in evoluzione, con l’obiettivo di rilevare early warning su nuovi tipi di eventi potenzialmente rischiosi. Dimostriamo la perfetta integrazione di queste diverse metodologie in un approccio completo alla gestione di OpRisk, promuovendo una strategia di mitigazione del rischio più olistica, lungimirante e adattiva., Operational risk (OpRisk) emerges as a pivotal non-financial concern with far-reaching implications for financial institutions. Departing from conventional regulatory tasks encompassing data collection, capital requirement calculations, and report generation for managerial decisions, OpRisk functions are now actively pursuing proactive strategies to forestall or alleviate risk impacts. For instance, artificial intelligence techniques, increasingly integral for managerial insights, are now employed to extract additional information from data. This study advances the application of text analysis techniques, a foundational element of Natural Language Processing, to OpRisk event descriptions. The present work introduces a structured workflow for the application of text analysis techniques to the OpRisk event descriptions to identify managerial clusters (more granular than regulatory categories) representing the root causes of the underlying OpRisks. However, these potent approaches exhibit limitations in influencing the impact of future loss events. In response, this research delves into the augmentation of traditional data sources, exploring alternative channels to identify potential events in their nascent stages and proactively manage their impact. An innovative facet involves the analysis of relevant tweets from X (formerly Twitter) for continuous scanning of the changing risk environment, aiming to detect early warnings about new types of potentially risky events. We demonstrate the seamless integration of these diverse methodologies into a comprehensive approach to OpRisk management, fostering a more holistic, forward-looking, and adaptive risk mitigation strategy.

Individual subjects’ ratings neither are metric nor have homogeneous meanings, consequently digital- labeled collections of subjects’ ratings are intrinsically ordinal and categorical. However, in these situations, the literature privileges the use of measures conceived for numerical data. In this paper, we discuss the exploratory theme of employing conditional entropy to measure degrees of uncertainty in responding to self-rating questions and that of displaying the computed entropies along the ordinal axis for visible pattern recognition. We apply this theme to the study of an online dataset, which contains responses to the Rosenberg Self-Esteem Scale. We report three major findings. First, at the fine scale level, the resultant multiple ordinal-display of response-vs-covariate entropy measures reveals that the subjects on both extreme labels (high self-esteem and low self-esteem) show distinct degrees of uncertainty. Secondly, at the global scale level, in responding to positively posed questions, the degree of uncertainty decreases for increasing levels of self-esteem, while, in responding to negative questions, the degree of uncertainty increases. Thirdly, such entropy-based computed patterns are preserved across age groups. We provide a set of tools developed in R that are ready to implement for the analysis of rating data and for exploring pattern-based knowledge in related research.

Recent evidence highlights the usefulness of DNA methylation (DNAm) biomarkers as surrogates for exposure to risk factors for noncommunicable diseases in epidemiological studies and randomized trials. DNAm variability has been demonstrated to be tightly related to lifestyle behavior and exposure to environmental risk factors, ultimately providing an unbiased proxy of an individual state of health. At present, the creation of DNAm surrogates relies on univariate penalized regression models, with elastic-net regularizer being the gold standard when accomplishing the task. Nonetheless, more advanced modeling procedures are required in the presence of multivariate outcomes with a structured dependence pattern among the study samples. In this work we propose a general framework for mixed-effects multitask learning in presence of high-dimensional predictors to develop a multivariate DNAm biomarker from a multicenter study. A penalized estimation scheme, based on an expectation-maximization algorithm, is devised in which any penalty criteria for fixed-effects models can be conveniently incorporated in the fitting process. We apply the proposed methodology to create novel DNAm surrogate biomarkers for multiple correlated risk factors for cardiovascular diseases and comorbidities. We show that the proposed approach, modeling multiple outcomes together, outperforms state-of-the-art alternatives both in predictive power and biomolecular interpretation of the results.

Road accidents represent a concern for modern societies, especially in poor and developing countries. In this paper, we develop a road safety model assuming that the car crashes recorded in Milan (Italy) during 2019 can be appropriately modelled as a realisation of a spatio-temporal point process on a linear network. We adopt a separable first-order intensity function with spatial and temporal components. The temporal dimension is estimated semi-parametrically using an additive Poisson regression model. The spatial dimension is estimated semi-parametrically considering a b-spline transformation of two potentially relevant space-varying covariates, namely the traffic flows and the distance to the closest road sign. This approach permits us to analyse traffic accidents at a very granular spatial scale, hence avoiding potential biases due to data aggregation.

In this paper we frame the problem of obtaining estimates from the sur- vey on the employment status of graduates in Italy as a Small Area Estimation problem because of unit nonresponse. We propose to use generalized linear mixed models and to include two variables that can be considered proxies of the response propensity among the set of covariates to make the MAR assumption more tenable. Estimates for degree programmes are obtained as (semi-parametric) empirical best predictions.

After a review of the class of discrete latent variable models in terms of formulation and estimation methods, recent advances and perspectives regarding these models are illustrated. We consider in detail the stochastic block model for social networks and models for spatio-temporal data. Among these developments, we discuss, in particular, the analysis of longitudinal compositional data about expenditures of the Spanish regions over several decades.

Italians are getting older and demand more and more attention on medical care. However, the need to curb public spending calls for a radical reorganisation of the Italian healthcare system. A study of the data available from the Istat - HFA (Health For All) data set reveals a general picture where it seems that supply is struggling to meet demand, pushing families towards a system of private care. A spatio-temporal regression model is presented to interpret the phenomenon and better understand the dynamics of the last two decades and better chart the future of our healthcare system. The resulting picture is that of a nation with different care needs per geographical area. The alpine areas and Rome Capital are the most important.

Matrix manipulation in Stata can be a time-consuming and tedious task, especially when it is necessary to subset or rearrange elements from large matrices based on nonconsecutive elements. Compared with Mata, these tasks require more time, more code, and sometimes more complex output. The purpose of this article is to introduce submatrix, a command to manipulate matrix elements using row (and column) names, numbers, and equations.

The present research explores the heterogeneity in trajectories of subjective well-being of Japanese citizens using longitudinal data collected with the Preference Parameters Study from 2003 to 2018. The analysis is carried out through the hidden Markov model that assumes a latent process underlying the individual perception of happiness observed through a categorical response variable. The first-order Markov chain is parameterized in terms of initial and transition probabilities depending on time-constant and time-varying socioeconomic and demographic variables. Maximum likelihood estimation of model parameters accounts for longitudinal sampling weights and missing responses under the Missing-At-Random assumption. Through this model-based clustering approach, we discover three clusters of individuals showing different dynamics across the life course, each of which represents, namely “not so happy”, “moderately happy”, and “very happy” individuals. We find that males tend to be less happy than females, and a U-shaped association between happiness and age is not detected. Each state has a substantial persistence over time, meaning that initial happiness perceptions play an important role in the life course inequalities of subjective well-being.

In longitudinal data analysis, hidden Markov (HM) models are fundamental tools, especially when the analysis is focused on transitions or the need to cluster individuals dynamically. When individual covariates are available in the dataset, a typical problem is how to parametrize the transition probabilities based on these covariates in a parsimonious way. In fact, standard multinomial parametrizations of these probabilities lead to models with many parameters, which are also difficult to interpret and, consequently, to unstable parameter estimates. To overcome the above problems, different parametrizations of the transition probabilities of HM models with covariates are introduced based on multinomial logit models formulated by two different choices of the reference state of each logit. These parametrizations rely on constraints having a straightforward interpretation, making the model much more parsimonious. Estimation based on the maximum likelihood (ML) approach is developed under different constraints based on the Expectation-Maximization algorithm. Steps of Newton-Raphson type are also included to improve the algorithm’s convergence speed

In this work, we introduce a general model for a collection of innovation processes in order to model and analyze the interaction among them. We provide theoretical results, analytically proven, and we show how the proposed model fits the behaviors observed in some real data sets (from Reddit and Gutenberg). It is worth mentioning that the given applications are only examples of the potentialities of the proposed model and related results: due to its abstractness and generality, it can be applied to many interacting innovation processes.

We propose assessing the causal effects of a dynamic treatment in a longitudinal observational study, given observed confounders under suitable assumptions. The causal hidden Markov model is based on potential versions of discrete latent variables, and it accounts for the estimated propensity to be assigned to each treatment level over time using inverse probability weighting. Estimation of the model parameters is carried out through a weighted maximum log-likelihood approach. Standard errors for the parameter estimates are provided by nonparametric bootstrap. The proposal is validated through a simulation study aimed at comparing different model specifications. As an illustrative example, we consider a marketing campaign conducted by a large European bank over time on its customers. Findings provide straightforward managerial implications.

We propose a spatio-temporal analysis aiming at estimating the variation of gasoline and diesel consumption occurred in the Italian provinces as a consequence of the COVID-19 pandemic during 2020 and 2021. We employ generalized linear models and generalized additive models to predict business-as-usual per capita fuel consumption by means of socio-economic variables, such as demography, tourist stays, temperature and territorial characteristics. The province-specific impact of the restrictions is then estimated as the difference between the observed and model-predicted values. The spatio-temporal dynamics is introduced by means of appropriate spline basis functions allowing both spatial and time trend to be smooth surfaces. Moreover, we include a smooth spatio-temporal interaction that properly capture the seasonal characteristic of different areas. Our findings highlight that the national mobility restrictions imposed to fight the spread of COVID-19 in the first wave (March to May 2020) reduced gasoline and diesel consumption homogeneously nationwide, with some slight differences between northern and southern provinces. However, the second wave lockdown (Winter 2020–2021) determined heterogeneous impacts across Italian provinces. In particular, we highlight the existence of a divergence between North and South Italy in terms of reaction to the pandemic. Indeed, while southern provinces experienced the weakest and less variable reductions, the northern provinces recorded strong and persistent contractions of fuel consumption. Also, southern and tourism-devoted provinces recovered quickly and compact to the post-pandemic reopenings.

Aim: The mechanisms governing the organism’s response to exercise are complex and difficult to study. Spectral analysis of heart rate variability (HRV) could represent a convenient methodology for studying humans’ autonomic nervous system (ANS). However, difficulties in interpreting the multitude of correlated HRV-derived indices, mainly when computed over different time segments, may represent a barrier to its usage. This preliminary investigation addressed to elite athletes proposes a novel method describing the cardiac autonomic response to exercise based on multilevel exploratory factor analysis (MEFA), which reduces the multitude of HRV-derived indices to fewer uncorrelated ANS indicators capable of accounting for their interrelationships and overcoming the above difficulties. Methods: The study involved 30 Italian Olympic athletes, divided into 15 cyclists (prevalent high-intensity endurance training) and 15 shooters (prevalent technical training with low-intensity endurance component). All athletes underwent a complete test of a dynamic protocol, constituted by a rest-stand test followed by a stepwise bicycle stress test subdivided into a single bout of progressive endurance (from aerobic to anaerobic) exercise and recovery. Then, by spectral analysis, values of 12 ANS proxies were computed at each time segment (9 epochs in all) of the complete test. Results: We obtained two global ANS indicators (amplitude and frequency), expressing the athletes’ overall autonomic response to the complete test, and three dynamic ANS indicators (amplitude, signal self-similarity, and oscillatory), describing the principal dynamics over time of the variability of RR interval (RRV). Globally, cyclists have significantly higher amplitude levels (median ± MAD: cyclists 69.9 ± 20.5; shooters 37.2 ± 19.4) and lower frequency levels (median ± MAD: cyclists 37.4 ± 14.8; shooters 78.2 ± 10.2) than shooters, i.e., a parasympathetic predominance compared to shooters. Regarding the RRV d

Road casualties represent an alarming concern for modern societies. During the last years, several authors proposed sophisticated approaches to help authorities implement new policies. These models were usually developed considering a set of socio-economic variables and ignoring the measurement error, which can bias the statistical inference. This paper presents a Bayesian model to analyse car crash occurrences at the network-lattice level, taking into account measurement error in the spatial covariate. The suggested methodology is exemplified by considering the collisions in the road network of Leeds (UK) during 2011–2019. Traffic volumes are approximated using an extensive set of counts obtained from mobile devices and the estimates are adjusted using a spatial measurement error correction.