On the geometry of Bayesian graphical models with hidden variables

Authors:
Raffaella Settimi;Jim Q. Smith
Affiliations:
Department of Statistics, University of Warwick, Coventry, UK;Department of Statistics, University of Warwick, Coventry, UK
Venue:
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Year:
1998

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Abstract

In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.