[ABE-L] Seminário - Modelos de Regressão e Aplicações -

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*Seminário - Modelos de Regressão e Aplicações*

*Título*: Invariant prior distributions for hierarchical models

*Palestrante*: Thais Fonseca – DME - UFRJ

*Quando*: 03 de agosto de 2018, sexta-feira, às 14h.

*Onde*: Sala 243 – Bloco A, segundo andar - IME-USP

*Resumo*. In this work, we propose an approach for constructing invariant
prior distributions for hierarchical models based on information geometry.
In particular, we provide a flexible decomposition for the Fisher
information tailored for multilevel models. This proposal takes advantage
of the hierarchy and leads to an alternative way of computing Jeffreys
priors for the hyperparameters besides providing an upper bound for the
prior information. While the Jeffreys prior gives the minimum information
about parameters, the proposed bound gives an upper limit for the
information put in the an objective prior. Any prior with information above
that limit may be considered too informative. Furthermore, the proposed
prior may be computed computationally as part of a MCMC algorithm. This
property might be essential in models with many levels in which analytical
marginalization is not feasible. As an alternative, we suggest an objective
prior which may be proper when the usual Jeffreys prior is not. We
illustrate the usefulness of our proposal with examples in mixture models,
in selection priors such as lasso and in the student-t model.
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