arXiv subjects

Fernando Andrés Quintana

Publications and source records attributed to Fernando Andrés Quintana.

8 recordsLinked to original sources

arXiv2026

Bayesian repulsive mixture model for multivariate functional data

We introduce a repulsive mixture model to cluster observation units represented by multivariate functional data, based on similarity of curve shapes and individual-specific covariates. We propose a repulsive prior distribution for the component-specific location parameters that depends on a B-spline curve-tailored distance, extending existent repulsive priors to the context of multivariate functional data. The proposed model favors the identification of well-differentiated clusters, avoiding the presence of redundant ones. To sample from the posterior distribution, we propose an MCMC algorithm that includes a novel split-merge step that significantly improves the chain mixing. Different features of the proposed model, including the effects of repulsion and covariates in the clustering, are evaluated through simulation. The proposed model is fitted to analyze Chronic Ankle Instability (CAI) data, focusing on identifing individuals with similar types of physical dysfunctions based on the similarity of movement patterns.

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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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arXiv2026

On the Validity of Isotropic Covariance Functions for Set-indexed Random Fields

Distances between sets arise naturally when modeling stochastic dependence on collections of spatial supports, including settings with point-referenced and areal observations. However, commonly used constructions of distances on sets, including those derived from the Hausdorff distance, generally fail to be conditionally negative definite, precluding their use in isotropic covariance models. We propose the ball--Hausdorff distance, defined as the Hausdorff distance between the minimum enclosing balls of bounded sets in a metric space. For length spaces, we derive an explicit representation of this distance in terms of the associated centers and radii. We show that the ball--Hausdorff distance is conditionally negative definite whenever the underlying metric is conditionally negative definite. By Schoenberg's theorem, this implies an isometric embedding into a Hilbert space and guarantees the validity of broad classes of isotropic covariance functions, including the Matérn and powered exponential families, for set-indexed random fields. The construction reduces dependence between sets to low-dimensional geometric summaries, leading to substantial simplifications in covariance evaluation.

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arXiv2025

Informed Random Partition Models with Temporal Dependence

Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit incorporating an ``initial'' partition informed by expert opinion. Then, using some similarity criteria, partitions different from the initial one are down weighted, i.e. they are assigned reduced probabilities. These methods represent an exciting new direction of method development in clustering techniques. We add to this literature a method that very flexibly permits assigning varying levels of uncertainty to any subset of the partition. This is particularly useful in practice as there is rarely clear prior information with regards to the entire partition. Our approach is not based on partition penalties but considers individual allocation probabilities for each unit (e.g., locally weighted prior information). We illustrate the gains in prior specification flexibility via simulation studies and an application to a dataset concerning spatio-temporal evolution of ${\rm PM}_{10}$ measurements in Germany.

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arXiv2024

A Bayesian multivariate model with temporal dependence on random partition of areal data

More than half of the world's population is exposed to the risk of mosquito-borne diseases, which leads to millions of cases and hundreds of thousands of deaths every year. Analyzing this type of data is often complex and poses several interesting challenges, mainly due to the vast geographic area, the peculiar temporal behavior, and the potential correlation between infections. Motivation stems from the analysis of tropical diseases data, namely, the number of cases of two arboviruses, dengue and chikungunya, transmitted by the same mosquito, for all the 145 microregions in Southeast Brazil from 2018 to 2022. As a contribution to the literature on multivariate disease data, we develop a flexible Bayesian multivariate spatio-temporal model where temporal dependence is defined for areal clusters. The model features a prior distribution for the random partition of areal data that incorporates neighboring information, thus encouraging maps with few contiguous clusters and discouraging clusters with disconnected areas. The model also incorporates an autoregressive structure and terms related to seasonal patterns into temporal components that are disease and cluster-specific. It also considers a multivariate directed acyclic graph autoregressive structure to accommodate spatial and inter-disease dependence, facilitating the interpretation of spatial correlation. We explore properties of the model by way of simulation studies and show results that prove our proposal compares well to competing alternatives. Finally, we apply the model to the motivating dataset with a twofold goal: clustering areas where the temporal trend of certain diseases are similar, and exploring the potential existence of temporal and/or spatial correlation between two diseases transmitted by the same mosquito.

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arXiv2023

Regression with Variable Dimension Covariates

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the ubiquitous nature of regression problems and the abundance of related methods and results there is a surprising gap in the literature. There are no well established methods for regression with a varying dimension covariate vectors, despite the common occurrence of such problems. In this paper we review some recent related papers proposing varying dimension regression by way of random partitions.

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arXiv2023

A Projection Approach to Local Regression with Variable-Dimension Covariates

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that utilizes only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject's incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model's effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data.

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arXiv2021

Multipartition model for multiple change point identification

Among the main goals in multiple change point problems are the estimation of the number and positions of the change points, as well as the regime structure in the clusters induced by those changes. The product partition model (PPM) is a widely used approach for the detection of multiple change points. The traditional PPM assumes that change points split the set of time points in random clusters that define a partition of the time axis. It is then typically assumed that sampling model parameter values within each of these blocks are identical. Because changes in different parameters of the observational model may occur at different times, the PPM thus fails to identify the parameters that experienced those changes. A similar problem may occur when detecting changes in multivariate time series. To solve this important limitation, we introduce a multipartition model to detect multiple change points occurring in several parameters at possibly different times. The proposed model assumes that the changes experienced by each parameter generate a different random partition of the time axis, which facilitates identifying which parameters have changed and when they do so. We discuss a partially collapsed Gibbs sampler scheme to implement posterior simulation under the proposed model. We apply the proposed model to identify multiple change points in Normal means and variances and evaluate the performance of the proposed model through Monte Carlo simulations and data illustrations. Its performance is compared with some previously proposed approaches for change point problems. These studies show that the proposed model is competitive and enriches the analysis of change point problems.

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