Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 1, 43--55

Bayesian Inference For Nondecomposable Graphical Gaussian Models

By

Petros Dellaportas, Athens University Of Economics And Business, Greece

Paolo Giudici, University Of Pavia, Italy And

Gareth Roberts, University Of Cambridge, Uk

SUMMARY. In this paper we propose  a  method to calculate the posterior probability of a nondecomposable graphical Gaussian model. Our proposal is based on a new device to sample from  Wishart distributions, conditional on the graphical constraints. As a result, our  methodology allows Bayesian model selection within the {\em whole} class  of graphical Gaussian models, including nondecomposable ones.

AMS (1991) subject classification. 62F15,60EO5.

Key words and phrases. Importance sampling, partial correlation coefficient, sampling from conditional Wishart distibution.

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