arXiv subjects

Alessandra Guglielmi

Publications and source records attributed to Alessandra Guglielmi.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Mixture Models for Histograms: with Applications to Large Datasets

In many real-world scenarios, especially those involving privacy constraints or data summarization, data are available only in aggregated forms, such as histograms or frequency tables. This work introduces a novel Bayesian method for inferring the underlying population distribution by fitting a mixture model to binned data. While we focus on mixtures of normal distributions, the framework is flexible and can be extended to other distributional families. We place a prior distribution on the number of mixture components, accommodating both finite and countably infinite mixtures, and perform inference using reversible jump MCMC. The proposed approach demonstrates strong performance on large-scale data, showcasing the potential of nonparametric Bayesian modeling in practical applications. Furthermore, we extend the method to model multiple histograms simultaneously and cluster them using the Dirichlet process. This enables information sharing across populations and provides a principled posterior probability to assess homogeneity between groups. Some theoretical results supporting the performance of our proposed methodology are also discussed.

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arXiv2026

A warning system for risk prediction of metabolic syndrome in a healthy population of blood donors

Metabolic syndrome is a complex clinical condition characterized by the simultaneous presence of multiple metabolic risk factors and represents a major public health concern. The syndrome develops silently and may remain undiagnosed for long periods, highlighting the importance of investigating early metabolic alterations before overt disease onset. Longitudinal monitoring of predominantly healthy individuals may help identify metabolic risk early. The paper proposes a Bayesian statistical model to estimate the probability of metabolic syndrome among blood donors during pre-donation screening, incorporating information collected at previous visits. Using longitudinal data from one of the main blood donor associations in Italy, AVIS Milan, we analyze repeated clinical and lifestyle measurements from a predominantly healthy population of donors. In particular, we fit a Bayesian multivariate model that jointly represents the logarithm of the five diagnostic components of metabolic syndrome. The model accounts for within-donor dependence across repeated visits and provides probabilistic estimates of individual risk. Our framework aims to provide clinicians at AVIS Milan with an interpretable traffic-light warning system (low, intermediate, high risk) during pre-donation screening to facilitate the identification of individuals at risk of metabolic syndrome at future visits and to support targeted preventive interventions during routine donor assessment, ultimately contributing to a long-term reduction in healthcare costs for the Italian national healthcare system.

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arXiv2026

Bayesian nonparametric boundary detection for multiple areal data

We consider the problem of boundary detection for areal data, focusing on situations where for each areal unit multiple observations are available. We propose a Bayesian nonparametric mixture model for the area-specific population densities, with spatially dependent weights and a random number of components. Contrary to previously proposed methods for boundary detection, which consider one observation per areal unit, ours does not require external information such as area-specific covariates or dissimilarity metrics. Instead, by exploiting information from multiple samples per area, it is able to identify boundaries between areas that exhibit different densities. Crucially, the number of mixture components needs to be learned from data to obtain meaningful boundary detection, due to the non-identifiability of overfitted mixtures. Therefore, we assume it random by placing a prior on it. The motivating application is the analysis of economic inequality in the greater Los Angeles region, which typically yields social inequality and unrest. Efficient posterior computation is facilitated by a transdimensional Markov Chain Monte Carlo sampler which exploits the recently introduced optimal auxiliary priors to improve the mixing. The methodology is validated via extensive simulations and applied to the income data in the greater Los Angeles region. We identify several boundaries in the income distributions, which can be explained ex-post in terms of the percentage of the population without health insurance, though not in terms of the total number of crimes, showing the usefulness of such an analysis to policymakers.

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arXiv2026

A Bayesian time-varying random partition model for large spatio-temporal datasets

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated, according to a specific neighbouring structure. Motivated by a dataset on mobile phone usage in the Metropolitan area of Milan, Italy, we propose a semi-parametric hierarchical Bayesian model allowing for time-varying as well as spatial model-based clustering. Our approach incorporates the notion of regimes that describe changing patterns over work and night hours as well as weekdays/weekends. Changes across regimes are considered by means of temporal changepoint components that allow for different hierarchical structures specified across time points. The changepoints might occur within fixed time windows over the day. The model features a novel random partition prior that incorporates the desired spatial features and encourages co-clustering based on areal proximity. We explore properties of the model by way of extensive simulation studies from which we collect valuable information. Finally, we discuss the application to the motivating data, where the main goal is to spatially cluster population patterns of mobile phone usage.

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arXiv2025

Bayesian Source Apportionment of Spatio-temporal air pollution data

Understanding the sources that contribute to fine particulate matter (PM$_{2.5}$) is of crucial importance for designing and implementing targeted air pollution mitigation strategies. Determining what factors contribute to a pollutant's concentration goes under the name of source apportionment and it is a problem long studied by atmospheric scientists and statisticians alike. In this paper, we propose a Bayesian model for source apportionment, that advances the literature on source apportionment by allowing estimation of the number of sources and accounting for spatial and temporal dependence in the observed pollutants' concentrations. Taking as example observations of six species of fine particulate matter observed over the course of a year, we present a latent functional factor model that expresses the space-time varying observations of log concentrations of the six pollutant as a linear combination of space-time varying emissions produced by an unknown number of sources each multiplied by the corresponding source's relative contribution to the pollutant. Estimation of the number of sources is achieved by introducing source-specific shrinkage parameters. Application of the model to simulated data showcases its ability to retrieve the true number of sources and to reliably estimate the functional latent factors, whereas application to PM$_{2.5}$ speciation data in California identifies 3 major sources for the six PM$_{2.5}$ species.

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arXiv2025

Hierarchical shot-noise Cox process mixtures for clustering across groups

Clustering observations across partially exchangeable groups of data is a routine task in Bayesian nonparametrics. Previously proposed models allow for clustering across groups by sharing atoms in the group-specific mixing measures. However, exact atom sharing can be overly rigid when groups differ subtly, introducing a trade-off between clustering and density estimates and fragmenting across-group clusters, particularly at larger sample sizes. We introduce the hierarchical shot-noise Cox process (HSNCP) mixture model, where group-specific atoms concentrate around shared centers through a kernel. This enables accurate density estimation within groups and flexible borrowing across groups, overcoming the density-clustering trade-off of previous approaches. Our construction, built on the shot-noise Cox process, remains analytically tractable: we derive closed-form prior moments and an inter-group correlation, obtain the marginal law and predictive distribution for latent parameters, as well as the posterior of the mixing measures given the latent parameters. We develop an efficient conditional MCMC algorithm for posterior inference. We assess the performance of the HSNCP model through simulations and an application to a large galaxy dataset, demonstrating balanced across-group clusters and improved density estimates compared with the hierarchical Dirichlet process, including under model misspecification.

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arXiv2025

Bayesian Mixtures Models with Repulsive and Attractive Atoms

The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant interest in the context of Bayesian mixture models. This allows the definition of priors that encourage well-separated and interpretable clusters. In this work, we provide a unified framework for the construction and the Bayesian analysis of random probability measures with interacting atoms, encompassing both repulsive and attractive behaviours. Specifically, we derive closed-form expressions for the posterior distribution, the marginal and predictive distributions, which were not previously available except for the case of measures with i.i.d. atoms. We show how these quantities are fundamental both for prior elicitation and to develop new posterior simulation algorithms for hierarchical mixture models. Our results are obtained without any assumption on the finite point process that governs the atoms of the random measure. Their proofs rely on analytical tools borrowed from the Palm calculus theory, which might be of independent interest. We specialise our treatment to the classes of Poisson, Gibbs, and determinantal point processes, as well as in the case of shot-noise Cox processes. Finally, we illustrate the performance of different modelling strategies on simulated and real datasets.

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arXiv2024

Bayesian clustering of high-dimensional data via latent repulsive mixtures

Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked to the observations via a Gaussian latent factor model. This approach was recently investigated by Chandra et al. (2023). The authors use a factor-analytic representation and assume a mixture model for the latent factors. However, performance can deteriorate in the presence of model misspecification. Assuming a repulsive point process prior for the component-specific means of the mixture for the latent scores is shown to yield a more robust model that outperforms the standard mixture model for the latent factors in several simulated scenarios. The repulsive point process must be anisotropic to favor well-separated clusters of data, and its density should be tractable for efficient posterior inference. We address these issues by proposing a general construction for anisotropic determinantal point processes. We illustrate our model in simulations as well as a plant species co-occurrence dataset.

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arXiv2024

The Multivariate Bernoulli detector: Change point estimation in discrete survival analysis

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffer from biased estimation. Therefore, we propose the Multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a Multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from non-conjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

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arXiv2022

Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated according to a specific neighboring structure. Incorporating the temporal and spatial dimension into a statistical model poses challenges regarding the underlying theoretical framework as well as the implementation of efficient computational methods. We propose to include spatio-temporal random effects using a conditional autoregressive prior, where the temporal correlation is modeled through an autoregressive mean decomposition and the spatial correlation by the precision matrix inheriting the neighboring structure. Their joint distribution constitutes a Gaussian Markov random field, whose sparse precision matrix enables the usage of efficient sampling algorithms. We cluster the areal units using a nonparametric prior, thereby learning latent partitions of the areal units. The performance of the model is assessed via an application to study regional unemployment patterns in Italy. When compared to other spatial and spatio-temporal competitors, the proposed model shows more precise estimates and the additional information obtained from the clustering allows for an extended economic interpretation of the unemployment rates of the Italian provinces.

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arXiv2022

Clustering blood donors via mixtures of product partition models with covariates

Motivated by the problem of accurately predicting gap times between successive blood donations, we present here a general class of Bayesian nonparametric models for clustering. These models allow for prediction of new recurrences, accommodating covariate information that describes the personal characteristics of the sample individuals. We introduce a prior for the random partition of the sample individuals which encourages two individuals to be co-clustered if they have similar covariate values. Our prior generalizes PPMx models in the literature, which are defined in terms of cohesion and similarity functions. We assume cohesion functions which yield mixtures of PPMx models, while our similarity functions represent the compactness of a cluster. We show that including covariate information in the prior specification improves the posterior predictive performance and helps interpret the estimated clusters, in terms of covariates in the blood donation application.

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arXiv2022

Bayesian Functional Emulation of CO2 Emissions on Future Climate Change Scenarios

We propose a statistical emulator for a climate-economy deterministic integrated assessment model ensemble, based on a functional regression framework. Inference on the unknown parameters is carried out through a mixed effects hierarchical model using a fully Bayesian framework with a prior distribution on the vector of all parameters. We also suggest an autoregressive parameterization of the covariance matrix of the error, with matching marginal prior. In this way, we allow for a functional framework for the discretized output of the simulators that allows their time continuous evaluation.

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arXiv2022

BayesMix: Bayesian Mixture Models in C++

We describe BayesMix, a C++ library for MCMC posterior simulation for general Bayesian mixture models. The goal of BayesMix is to provide a self-contained ecosystem to perform inference for mixture models to computer scientists, statisticians and practitioners. The key idea of this library is extensibility, as we wish the users to easily adapt our software to their specific Bayesian mixture models. In addition to the several models and MCMC algorithms for posterior inference included in the library, new users with little familiarity on mixture models and the related MCMC algorithms can extend our library with minimal coding effort. Our library is computationally very efficient when compared to competitor software. Examples show that the typical code runtimes are from two to 25 times faster than competitors for data dimension from one to ten. Our library is publicly available on Github at https://github.com/bayesmix-dev/bayesmix/.

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arXiv2022

Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Overweight and obesity in adults are known to be associated with risks of metabolic and cardiovascular diseases. Because obesity is an epidemic, increasingly affecting children, it is important to understand if this condition persists from early life to childhood and if different patterns of obesity growth can be detected. Our motivation starts from a study of obesity over time in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight patterns taken every 6 months from birth. We propose a novel model that facilitates clustering by combining a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show the superiority of the model to capture patterns, compared to other alternatives. We apply the model to the motivating dataset, and discuss the main features of the detected clusters. We also compare alternative models with ours in terms of predictive performances.

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arXiv2021

JAGS, NIMBLE, Stan: a detailed comparison among Bayesian MCMC software

The aim of this work is the comparison of the performance of the three popular software platforms JAGS, NIMBLE and Stan. These probabilistic programming languages are able to automatically generate samples from the posterior distribution of interest using MCMC algorithms, starting from the specification of a Bayesian model, i.e. the likelihood and the prior. The final goal is to present a detailed analysis of their strengths and weaknesses to statisticians or applied scientists. In this way, we wish to contribute to make them fully aware of the pros and cons of this software. We carry out a systematic comparison of the three platforms on a wide class of models, prior distributions, and data generating mechanisms. Our extensive simulation studies evaluate the quality of the MCMC chains produced, the efficiency of the software and the goodness of fit of the output. We also consider the efficiency of the parallelization made by the three platforms.

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arXiv2021

The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I greater or equal than 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed.

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arXiv2021

Spatially dependent mixture models via the Logistic Multivariate CAR prior

We consider the problem of spatially dependent areal data, where for each area independent observations are available, and propose to model the density of each area through a finite mixture of Gaussian distributions. The spatial dependence is introduced via a novel joint distribution for a collection of vectors in the simplex, that we term logisticMCAR. We show that salient features of the logisticMCAR distribution can be described analytically, and that a suitable augmentation scheme based on the Pólya-Gamma identity allows to derive an efficient Markov Chain Monte Carlo algorithm. When compared to competitors, our model has proved to better estimate densities in different (disconnected) areal locations when they have different characteristics. We discuss an application on a real dataset of Airbnb listings in the city of Amsterdam, also showing how to easily incorporate for additional covariate information in the model.

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arXiv2021

MCMC computations for Bayesian mixture models using repulsive point processes

Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of well separated clusters. The most commonly used methods for posterior inference either require to fix a priori the number of components or are based on reversible jump MCMC computation. We present a general framework for mixture models, when the prior of the `cluster centres' is a finite repulsive point process depending on a hyperparameter, specified by a density which may depend on an intractable normalizing constant. By investigating the posterior characterization of this class of mixture models, we derive a MCMC algorithm which avoids the well-known difficulties associated to reversible jump MCMC computation. In particular, we use an ancillary variable method, which eliminates the problem of having intractable normalizing constants in the Hastings ratio. The ancillary variable method relies on a perfect simulation algorithm, and we demonstrate this is fast because the number of components is typically small. In several simulation studies and an application on sociological data, we illustrate the advantage of our new methodology over existing methods, and we compare the use of a determinantal or a repulsive Gibbs point process prior model.

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