13,309 research outputs found
An empirical Bayes procedure for the selection of Gaussian graphical models
A new methodology for model determination in decomposable graphical Gaussian
models is developed. The Bayesian paradigm is used and, for each given graph, a
hyper inverse Wishart prior distribution on the covariance matrix is
considered. This prior distribution depends on hyper-parameters. It is
well-known that the models's posterior distribution is sensitive to the
specification of these hyper-parameters and no completely satisfactory method
is registered. In order to avoid this problem, we suggest adopting an empirical
Bayes strategy, that is a strategy for which the values of the hyper-parameters
are determined using the data. Typically, the hyper-parameters are fixed to
their maximum likelihood estimations. In order to calculate these maximum
likelihood estimations, we suggest a Markov chain Monte Carlo version of the
Stochastic Approximation EM algorithm. Moreover, we introduce a new sampling
scheme in the space of graphs that improves the add and delete proposal of
Armstrong et al. (2009). We illustrate the efficiency of this new scheme on
simulated and real datasets
Flexible covariance estimation in graphical Gaussian models
In this paper, we propose a class of Bayes estimators for the covariance
matrix of graphical Gaussian models Markov with respect to a decomposable graph
. Working with the family defined by Letac and Massam [Ann.
Statist. 35 (2007) 1278--1323] we derive closed-form expressions for Bayes
estimators under the entropy and squared-error losses. The family
includes the classical inverse of the hyper inverse Wishart but has many more
shape parameters, thus allowing for flexibility in differentially shrinking
various parts of the covariance matrix. Moreover, using this family avoids
recourse to MCMC, often infeasible in high-dimensional problems. We illustrate
the performance of our estimators through a collection of numerical examples
where we explore frequentist risk properties and the efficacy of graphs in the
estimation of high-dimensional covariance structures.Comment: Published in at http://dx.doi.org/10.1214/08-AOS619 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Hierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data
We address the problem of analyzing sets of noisy time-varying signals that
all report on the same process but confound straightforward analyses due to
complex inter-signal heterogeneities and measurement artifacts. In particular
we consider single-molecule experiments which indirectly measure the distinct
steps in a biomolecular process via observations of noisy time-dependent
signals such as a fluorescence intensity or bead position. Straightforward
hidden Markov model (HMM) analyses attempt to characterize such processes in
terms of a set of conformational states, the transitions that can occur between
these states, and the associated rates at which those transitions occur; but
require ad-hoc post-processing steps to combine multiple signals. Here we
develop a hierarchically coupled HMM that allows experimentalists to deal with
inter-signal variability in a principled and automatic way. Our approach is a
generalized expectation maximization hyperparameter point estimation procedure
with variational Bayes at the level of individual time series that learns an
single interpretable representation of the overall data generating process.Comment: 9 pages, 5 figure
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