Carlos Matrán

Del Barrio, E., Cuesta-Albertos, J. A., Hallin, M., & Matrán, C. (2026). Cuantiles multivariantes, rangos y transporte de medidas. Boletín de Estadística e Investigación Operativa, 42(1), 8-23. https://doi.org/10.63552/beio.2026.42.1.02

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal Directions. This and other similarity criteria that arise from the spectral decomposition of a matrix are the bases of the Parsimonious Model. We show that such groupings of covariance matrices can be achieved through simple modifications of the CEM (Classification Expectation Maximization) algorithm. Our approach leads to propose Gaussian Mixture Models for model-based clustering and discriminant analysis, in which covariance matrices are clustered according to a parsimonious criterion, creating intermediate steps between the fourteen widely known parsimonious models. The added versatility not only allows us to obtain models with fewer parameters for fitting the data, but also provides greater interpretability. We show its usefulness for model-based clustering and discriminant analysis, providing algorithms to find approximate solutions verifying suitable size, shape and orientation constraints, and applying them to both simulation and real data examples.

Background: Data obtained from flow cytometry present pronounced variability due to biological and technical reasons. Biological variability is a well-known phenomenon produced by measurements on different individuals, with different characteristics such as illness, age, sex, etc. The use of different settings for measurement, the variation of the conditions during experiments and the different types of flow cytometers are some of the technical causes of variability. This mixture of sources of variability makes the use of supervised machine learning for identification of cell populations difficult. The present work is conceived as a combination of strategies to facilitate the task of supervised gating. Results: We propose optimalFlowTemplates, based on a similarity distance and Wasserstein barycenters, which clusters cytometries and produces prototype cytometries for the different groups. We show that supervised learning, restricted to the new groups, performs better than the same techniques applied to the whole collection. We also present optimalFlowClassification, which uses a database of gated cytometries and optimalFlowTemplates to assign cell types to a new cytometry. We show that this procedure can outperform state of the art techniques in the proposed datasets. Our code is freely available as optimalFlow, a Bioconductor R package at https://bioconductor.org/packages/optimalFlow. Conclusions: optimalFlowTemplates + optimalFlowClassification addresses the problem of using supervised learning while accounting for biological and technical variability. Our methodology provides a robust automated gating workflow that handles the intrinsic variability of flow cytometry data well. Our main innovation is the methodology itself and the optimal transport techniques that we apply to flow cytometry analysis.

Project Euclid - mathematics and statistics online

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in statistics through natural questions such as “Is the the new treatment significantly better than the old?” However, this is only partially answered by some of the usual statistical tools for this task. More importantly, often practitioners are not aware of the real meaning behind these statistical procedures. We analyze these troubles from the point of view of the order between distributions, the stochastic order, showing evidence of the limitations of the usual approaches, paying special attention to the classical comparison of means under the normal model. We discuss the unfeasibility of statistically proving stochastic dominance, but show that it is possible, instead, to gather statistical evidence to conclude that slightly relaxed versions of stochastic dominance hold.