|
Seminário
PIPGEs - UFSCar/USP ? 04/10/2013 - 14h00 LOCAL:
Sala
de Seminários 1 ? Prédio Anexo do DEs-UFSCar
TÍTULO:
Objective Bayesian
analysis for heteroscedastic PALESTRANTE:
Helio dos Santos
Migon - UFRJ RESUMO:
In many statistical
problems the normality assumption is very common but in many cases untenable for
natural phenomena due to the distribution of the data shows a leptokurtic or a
platykurtic shape and is not robust to outliers. In that context, more flexible
models can be adopted to accommodate this characteristic. One alternative is to
use location-scale models with heavy-tailed prior distributions like Student-t,
exponential power between others. The use of Student t-distribution for error
component is a good alternative because it provides more flexible tails and
reduces the influence of outliers and robust analysis from a Bayesian point of
view is possible, for example, for regression model. Sometimes a better choice
is the exponential power (EP) distribution that can provide both heavier
(leptokurtic) and lighter tails (platykurtic) than normal density. In that
context, we develop objective Bayesian analysis for linear heteroscedastic
regression models. More specifically, we derive explicit expressions for
Jeffreys priors for the model parameters. For both, Student-t and EP
distributions, we show that some of these Jeffreys priors lead to a proper
posterior distributions. Moreover, we show that our proposed Bayesian analysis
compares favorably to frequentist analysis previously proposed in the
literature. Finally, we illustrate our methodology with applications of the
Student-t and exponential power regression models to different
datasets. |