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Current issue: volume 49 (2), July-December 2025

  • A stochastic partial differential equation for Bayesian spatio-temporal modelling of crime

    Julia Calatayud, Marc Jornet, Javier Platero and Jorge Mateu

    Abstract: We propose a stochastic partial differential equation to model geo-referenced data in the plane, with spatially correlated noise and a temporal log-normal evolution. Discretization in space permits us to develop the model in a finite-dimensional framework, reducing it to a set of stochastic differential equations coupled by correlated Wiener processes. The correlations are considered time-varying and stochastic, with a transformed log-normal distribution. The final model is framed within a hierarchical structure, and parameter inference is conducted jointly using Bayesian methods. The statistical methodology is illustrated by analyzing crime activity in the city of Valencia, Spain.

    Keywords: Bayesian inference, crime time series, lattice data, space-time correlation, space-time intensity, stochastic log-Gaussian model, stochastic partial differential equation

    Pages: 149–178

    DOI: 10.57645/20.8080.02.26

  • Optimism correction of the area under the ROC curve, with missing data

    Susana Rafaela Martins, María del Carmen Iglesias-Pérez and Jacobo de Uña-Álvarez

    Abstract: The area under the ROC curve (AUC) plays an important role in the study of the predictive capacity of regression models. It is well known that an inflated AUC may result when the same data are used for training and testing the model. In this paper optimism correction of the AUC in the presence of missing data is investigated. Complete case analysis, inverse probability weighting and multiple imputation are employed to address the issue of missing data. For each of these approaches, split-sample, K-fold cross-validation and leave-one-out cross-validation are employed to correct for the optimism of the AUC. The methods are compared through intensive Monte Carlo simulations in the particular setting of binary regression. Results suggest that all estimators are consistent with the exception of complete case analysis, which may be biased when missing is not completely at random. In general, a combined application of multiple imputation and leave-one-out cross-validation is recommended.

    Keywords: cross-validation, logistic regression, missing values, multiple imputation, prediction

    Pages: 179–212

    DOI: 10.57645/20.8080.02.27

  • On generalized Gower distance for mixed-type data: extensive simulation study and new software tools

    Aurea Grané and Fabio Scielzo-Ortiz

    Abstract: Data scientists address real-world problems using multivariate and heterogeneous data-sets, characterized by multiple variables of different natures. Selecting a suitable distance function between units is crucial, as many statistical techniques and machine learning algorithms depend on this concept. Traditional distances, such as Euclidean or Manhattan, are unsuitable for mixed-type data, and although Gower distance was designed to handle this kind of data, it may lead to suboptimal results in the presence of outlying units or underlying correlation structure. In this work robust distances for mixed-type data are defined and explored, namely robust generalized Gower and robust related metric scaling. A new Python package is developed, which enables to compute these robust proposals as well as classical ones.

    Keywords: distances, generalized Gower, multivariate heterogeneous data, outliers, robust Mahalanobis, related metric scaling

    Pages: 213–244

    DOI: 10.57645/20.8080.02.28

  • Bayesian estimation for conditional probabilities associated to directed acyclic graphs: study of hospitalization of severe influenza cases

    Lesly Acosta and Carmen Armero

    Abstract: This paper presents a Bayesian framework to estimate joint, conditional, and marginal probabilities in directed acyclic graphs to study the progression of hospitalized patients with confirmed severe influenza. Using data from the PIDIRAC retrospective cohort in Catalonia, we model patient pathways from admission to discharge, death, or transfer. Transition probabilities are estimated using a Bayesian Dirichlet-multinomial approach, while posterior distributions for absorbing states or inverse probabilities are assessed via simulation. Bayesian methodology quantifies uncertainty through posterior distributions, offering insights into disease progression and in improving hospital planning. These findings support more effective patient management and informed decision making during seasonal influenza outbreaks.

    Keywords: confirmed influenza hospitalization, directed acyclic graphs (DAGs), Dirichlet-multinomial Bayesian inferential process, healthcare decision-making, transition probabilities

    Pages: 245–264

    DOI: 10.57645/20.8080.02.29

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