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Graphical models based on vines: from partial correlation representations of Gaussian models to high-dimensional copulas

Tuesday, February 25, 2014 - 11:00
Harry Joe, Professor, Department of Statistics, UBC
Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

Speaker:  Harry Joe

This presentation will consist of introductory material to show partial correlation representations in Gaussian autoregressive, truncated vine, common factor, structured factor, and structural equation models. There is a dependence and graphical parametrization that should have applications in many areas.

Comparisons will be made of various types of graphical models, including Whittaker's Gaussian graphical model based on the inverse correlation matrix, vines with/without latent variables, and path diagrams for structural equation models.  The extension from partial correlation representations to high-dimensional copula models will be indicated. Vines have mainly been used for flexible high-dimensional copula models and lead to new ways of viewing Gaussian dependence models.

The key ideas are the following.

(i) The partial correlation parametrization for Gaussian dependence models.

(ii) The mixing of conditional distributions as the copula extension of partial correlations.

(iii) The substitution of a bivariate copula for each partial correlation combined with the sequential mixing of conditional distributions to get the vine copula extension of multivariate Gaussian, even if there are latent variables.