Robust graphical modeling of gene networks using classical and alternative T-distributions

Details Robust graphical modeling of gene networks using classical and alternative T-distributions Robust graphical modeling of gene networks using classical and alternative T-distributions

2010-09-19

arxiv.org/abs/1009.3669v3

Annals of Applied Statistics 2011, Vol. 5, No. 2A, 1057-1080

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/10-AOAS410 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/10-AOAS410

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of the likelihood function. In this paper we advocate the use of multivariate $t$-distributions for more robust inference of graphs. In particular, we demonstrate that penalized likelihood inference combined with an application of the EM algorithm provides a computationally efficient approach to model selection in the $t$-distribution case. We consider two versions of multivariate $t$-distributions, one of which requires the use of approximation techniques. For this distribution, we describe a Markov chain Monte Carlo EM algorithm based on a Gibbs sampler as well as a simple variational approximation that makes the resulting method feasible in large problems.

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