3,083 research outputs found
Robust graphical modeling of gene networks using classical and alternative T-distributions
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 -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 -distribution case. We consider two versions of
multivariate -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.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS410 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Large deviations of an infinite-server system with a linearly scaled background process
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening. Keywords: Queues; Infinite-server systems; Markov modulation; Large deviation
Tail estimates for homogenization theorems in random media
It is known that a random walk on among i.i.d. uniformly elliptic
random bond conductances verifies a central limit theorem. It is also known
that approximations of the covariance matrix can be obtained by considering
periodic environments. Here we estimate the speed of convergence of this
homogenization result. We obtain similar estimates for finite volume
approximations of the effective conductance and of the lowest Dirichlet
eigenvalue. A lower bound is also given for the variance of the Green function
of a random walk in a random non-negative potential.Comment: 26 page
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