Fecha: 21 de Enero de 2022 (Viernes)
Lugar: Canal YouTube Facultad de ciencias
Expositor: Hector Manuel Zarate, Profesor Titular, Universidad Nacional de Colombia
Título: Semiparametric Bayesian Approximation of Parameters in the Bi-parametric Exponential Family and Skew-Normal Distributions.
Complexity in statistical modeling is related mainly to non-standard data structures, real-time estimation, the presence of latent or hidden variables, and big-data issues. These increasing demands in the real world have caused semiparametric modeling to play a crucial role in contemporary statistical analysis. This work proposes a unified methodology to jointly infer the mean, uncertainty, and skewness functions in semiparametric models when the response variable comes from a two-parameter exponential family or an asymmetric distribution. Thus, we implemented Bayesian methods based on MCMC sampling techniques and deterministic variational learning algorithms. In these settings, each sub-model depends on some covariates parametrically and for others in a non-parametrically way. It follows that understanding how the moments change with predictors is a goal of Statistics, and it is of intrinsic interest given the role in approximating other quantities.
We examine several modeling scenarios that benefit from the fusion of the graphical models’ approach to Bayesian semiparametric regression under the architecture of GLM models. The significance and implications of our strategy lie in its potential to contribute to a unified computational methodology that provides insight into many complex models that otherwise could be intractable analytically. Therefore, combining data models and algorithms contribute to solving real-world problems enjoying crucial advantages related to faster computation time, which allow not only to quickly explore many models for the data but to estimate them accurately.