Seminario de Modelamiento Matemático

The goal of this seminar series is to attract scientists working at the frontier between pure mathematics tools and statistical modeling.
The emphasis of this interdisciplinary seminar is twofold. First we aim to highlight new mathematical approaches that improve the understanding of the properties of complex statistical models. Secondly we aim to explore strengths and limitations of statistical methods from a pure mathematical perspective.

This seminar is held on wednesdays at 17:00 hrs in room 1 of the Faculty of Mathematics

Reinaldo B. Arellano-Valle. PUC Chile
Scale and Shape Mixtures of Multivariate Skew-Normal Distributions
Sala 1,
We introduce a broad and flexible class of multivariate distributions obtained by both scale and shape mixtures of multivariate skew-normal distributions. We present the probabilistic properties of this family of distributions in detail and lay down the theoretical foundations for subsequent inference with this model. In particular, we study linear transformations, marginal distributions, stochastic representations and hierarchical representations.

We also describe an EM-type algorithm for maximum likelihood estimation of the parameters of the model and demonstrate its implementation on a wind dataset. Our family of multivariate distributions unifies and extends many existing models of the literature that can be seen as submodels of our proposal.
Joint work with: Clécio S. Ferreira1, Department of Statistics, Federal University of Juiz de Fora, Juiz de Fora, Brazil. Marc G. Genton2, CEMSE Division, King Abdullah University of Science and Technology, Thuwal,
Saudi Arabia.
[1] Arellano-Valle, R. B., Ferreira, C. S., and Genton, M. G. (2018) Scale and shape mixtures of multivariate skew-normal distributions, Journal of Multivariate Analysis, 166, 98-110.
Elsa Cazelles . CMM (Center for Mathematical Modelling)
Statistical properties of regularized barycenters in the Wasserstein space and application to the registration of flow cytometry data.
Sala 1, Edificio Rolando Chuaqui, Campus San Joaquín, Avda. Vicuña Mackenna 4860, Macul, Chile.
In this talk, we discuss the study of data that can be described by random probability measures (discrete or absolutely continuous) with support on Rd. The aim is to provide a first order statistical analysis on this space endowed with the Wasserstein distance, which boils down tothe study of the Frechet mean (or barycenter). In particular, we focus on the case of discrete data (or observations) sampled from absolutely continuous probability measures (a.c.) with respect to the Lebesgue measure. We thus introduce an estimator of the barycenter of random measures, penalized by a convex function, making it possible to enforce its a.c.
Another estimator is regularized by adding entropy when computing the Wasserstein distance (which has first been introduced for computational reasons). We are particularly interested in controlling the variance of these estimators.
Thanks to these results, the principle of Goldenshluger and Lepski allows us to obtain an automatic calibration of the regularization parameters. We then apply this work to the registration of multivariate densities, especially for flow cytometry data.
Claire Delplancke. Center of Mathematical Modeling in Santiago, Universidad de Chile
Bayesian Modeling for Inverse Problems? The Example of a Scalable Algorithm for Passive Seismic Tomography in Mining.
Sala 1, Edificio Rolando Chuaqui, Campus San Joaquín, Avda. Vicuña Mackenna 4860, Macul, Chile.