Estimation of means in graphical Gaussian models with symmetries

We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose corresponding means are restricted to being identical. We find a necessary and sufficient condition on the partition to ensure equality between the maximum likelihood and least-squares estimators of the mean.Comment: Published in at http://dx.doi.org/10.1214/12-AOS991 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference in Graphical Gaussian Models with Edge and Vertex Symmetries with the gRc Package for R

In this paper we present the R package gRc for statistical inference in graphical Gaussian models in which symmetry restrictions have been imposed on the concentration or partial correlation matrix. The models are represented by coloured graphs where parameters associated with edges or vertices of same colour are restricted to being identical. We describe algorithms for maximum likelihood estimation and discuss model selection issues. The paper illustrates the practical use of the gRc package.

On Exchangeability in Network Models

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size.Comment: Dedicated to the memory of Steve Fienber

Inference in Graphical Gaussian Models with Edge and Vertex Symmetries with the gRc Package for R

In this paper we present the R package gRc for statistical inference in graphical Gaussian models in which symmetry restrictions have been imposed on the concentration or partial correlation matrix. The models are represented by coloured graphs where parameters associated with edges or vertices of same colour are restricted to being identical. We describe algorithms for maximum likelihood estimation and discuss model selection issues. The paper illustrates the practical use of the gRc package

Propagation of Probabilities, Means and Variances in Mixed Graphical Association Models

A scheme is presented for modelling and local computation of exact probabilities, means and variances for mixed qualitative and quantitative variables. The models assume that the conditional distribution of the quantitative variables, given the qualitative, is multivariate Gaussian. The computational architecture is set up by forming a tree of belief universes, and the calculations are then performed by local message passing between universes. The asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure. Approximate methods when these are not appropriately fulfilled are sketched. Lauritzen and Spiegelhalter (1988) showed how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation, thereby paving the way for exploiting probability based models as parts of realistic systems for planning and decision support. The technique was subsequently imp..