Seminarios

Futuros Eventos

2019-03-22
12:00 hrs.
Seminario de Estadística
Debajyoti Sinha. Florida State University
Semiparametric Bayesian Latent Variable Regression for Skewed Multivariate Data
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chile
Abstract:
For many real-life studies with skewed multivariate responses, the level of skewness and association structure assumptions are essential for evaluating the covariate eff ects on the response and its predictive distribution. We present a novel semiparametric multivariate model and associated Bayesian analysis for multivariate skewed responses. Similar to multivariate Gaussian, this multivariate model is closed under marginalization, allows a wide class of multivariate associations, and has meaningful physical interpretations of skewness levels and covariate eff ects on the marginal density. Other desirable properties of our model include the Markov Chain Monte Carlo computation through available statistical software, and the assurance of consistent Bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions. We illustrate the practical advantages of our methods over existing alternatives via simulation studies, the analysis of a clinical study on periodontal disease and extensions to Bayesian regression trees.

This is a joint work with Drs. A.Bhingare, S.Lipsitz, D.Bandopadyay and A.Linero.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
http://midas.mat.uc.cl
2019-03-13
15:45 hrs.
Seminario Fismat
Monika Anna Winklmeier. Universidad de los Andes
Tba
Sala 5
2019-03-06
15:45 hrs.
Seminario Fismat
Christian Jaekel. University of São Paulo
On Reflection Positivity, Modular Localisation and Connes Cocycles
Sala 5
Abstract:
The unitary irreducible representations of the Lorentz group carry an intrinsic notion of localisation on de Sitter space, known as modular localisation. An extension of Araki’s perturbation theory of modular automorphisms can be used to define interacting representations of the Lorentz group, as well as the corresponding Haag-Kastler nets. The analyticity properties of the correlation functions allow us to extend these theories to “nets" of (non-abelian) von Neumann algebras on the sphere. Reflection positivity can be used to recover the interacting quantum (field) theories on the de Sitter space from the sphere. Explicit examples are scalar bosons with polynomial or exponential interactions in 1+1 space-time dimensions, but our aim is to classify all interacting quantum theories compatible with the space-time symmetries. The Minkowski space limit is the limit of space-time curvature to zero, which is well-behaved on the level of local von Neumann algebras.

Eventos Pasados

2019-01-25
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Diego Izquierdo. Mpim Bonn
Dimensión de los cuerpos, K-teoría y aritmética de los espacios homogéneos
Abstract:
En 1986, Kato y Kuzumaki hicieron varias conjecturas con las que esperaban dar una caracterización diofántica de la dimensión cohomológica de los cuerpos en términos de K-teoría de Milnor y de puntos racionales sobre hipersuperficies proyectivas de pequeño grado. Hoy en día, sabemos que estas conjecturas son falsas en general. En esta charla, veremos que si uno sustituye las hipersuperficies proyectivas de pequeño grado por los espacios homogéneos, la conjectura de Kato y Kuzumaki se vuelve cierta. Se trata de un trabajo en colaboración con Giancarlo Lucchini Arteche.
Sala 2
2019-01-14
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Piecewice chaotic maps
Abstract:
We will consider the class of Cr unidimensional piecewise maps with a transitive attractor. These maps can have simultaneously discontinuities, criticalities and singularities. We will show that topological chaos is equivalent to metric chaos. We recall that this result is known in several classes strictly contained in the general class that we are presenting.
Sala 2
2019-01-11
12:00 hrs.
Seminario de Estadística
David Dahl. Department of Statistics, Brigham Young University
Summarizing Distributions of Latent Structure
Abstract:
In a typical Bayesian analysis, consider effort is placed on "fitting the model" (e.g., obtaining samples from the posterior distribution) but this is only half of the inference problem.  Meaningful inference usually requires summarizing the posterior distribution of the parameters of interest.  Posterior summaries can be especially important in communicating the results and conclusions from a Bayesian analysis to a diverse audience.  If the parameters of interest live in R^n, common posterior summaries are means, medians, and modes.  Summarizing posterior distributions of parameters with complicated structure is a more difficult problem.  For example, the "average" network in the posterior distribution on a network is not easily defined. This paper reviews methods for summarizing distributions of latent structure and then proposes a novel search algorithm for posterior summaries.  We apply our method to distributions on variable selection indicators, partitions, feature allocations, and networks.  We illustrate our approach in a variety of models for both simulated and real datasets.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chilehttp://midas.mat.uc.cl
2019-01-10
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Pseudo-Anosov diffeomorphisms
Abstract:
We will introduce pseudo Cr smooth structures on surfaces that will have the following property; the Pseudo-Anosov diffeomorphisms are uniformly Cr hyperbolic. We will conjecture that the Bochi-Mane theorem will extend to such pesudo C1 smooth structures recovering the duality of the result for all surfaces.
Sala 2
2019-01-10
12:00 hrs.
Seminario de Estadística
Dae-Jin Lee. Bcam - Basque Center for Applied Mathematics
Hierarchical modelling of patient-reported outcomes data based on the beta-binomial distribution
Abstract:
The beta-binomial distribution does not belong to the exponential family and, hence classical regression techniques cannot be used when dealing with outcomes following the mentioned distribution. In this talk, we propose and develop regression models based on the beta-binomial distribution for the analysis of U, J or inverse J-shaped discrete and bounded outcomes. In fact, although this work is focused on the analysis of patient-reported outcomes (PROs), which usually follow the mentioned distributional shapes, proposed models can also be extended to several fields. First of all, we make a review and comparison of existing beta-binomial regression approaches in independent data context, concluding that the marginal approach is the most adequate. However, PRO studies are usually carried out in a longitudinal framework, where patients' responses are measured over time. This leads to a multilevel or correlated data structure and consequently, we extend the marginal beta-binomial regression approach to the inclusion of random effects to accommodate the hierarchical structure of the data. We develop the estimation and inference procedure for the model proposal. Furthermore, we compare the performance of our proposal with similar approaches in the literature, showing that it gets better results in terms of reducing the bias of the estimates. We apply the model to a longitudinal Chronic Obstructive Pulmonary Disease study carried out at Galdakao Hospital in Biscay, Spain, reaching clinically and statistically relevant results about the evolution of the patients over time. PROs are usually obtained using rating scale questionnaires consisting of questions or items, grouped into one or more subscales, often called dimensions or domains. Therefore, we also propose a multivariate regression model based on the beta-binomial distribution for the joint analysis of all the longitudinal dimensions provided by different questionnaires. Finally, it is worth mentioning that we have implemented all the proposed regression models in the PROreg R- package which is available at CRAN.
Sala 1, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chile
2019-01-04
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Yuri Bilu. Université de Bordeaux
Singular units do not exist
Abstract:
In the first part, I will revise the classical theory of complex multiplication of elliptic curves (or C-lattices); in particular, I will define the notion of a singular modulus, the j-invariant of an elliptic curve (or a C-lattice) with complex multiplication.  According to the old result of Weber, a singular modulus is an algebraic integer. In the second part, I will briefly describe the recent work of Habegger, Kühne and myself proving that a singular modulus cannot be algebraic unit.
Sala 2
2019-01-03
16:00hrs.
Seminario de Análisis y Geometría
Armin Schikorra . University of Pittsburgh
Self-repulsive curvature energies for curves and surfaces: regularity theory and relation to harmonic maps
Abstract:
I will talk about a class of curvature energies for curves, the O'Hara energies, that are nonlocal in nature. In particular, I will present an approach for regularity theory of minimizers and critical points for these curves which is based on a relation to (fractional) harmonic maps. Then I will present some results towards attempts of generalizing this idea to surfaces.
Sala 2