92 research outputs found
Sparse covariance estimation in heterogeneous samples
Standard Gaussian graphical models (GGMs) implicitly assume that the
conditional independence among variables is common to all observations in the
sample. However, in practice, observations are usually collected form
heterogeneous populations where such assumption is not satisfied, leading in
turn to nonlinear relationships among variables. To tackle these problems we
explore mixtures of GGMs; in particular, we consider both infinite mixture
models of GGMs and infinite hidden Markov models with GGM emission
distributions. Such models allow us to divide a heterogeneous population into
homogenous groups, with each cluster having its own conditional independence
structure. The main advantage of considering infinite mixtures is that they
allow us easily to estimate the number of number of subpopulations in the
sample. As an illustration, we study the trends in exchange rate fluctuations
in the pre-Euro era. This example demonstrates that the models are very
flexible while providing extremely interesting interesting insights into
real-life applications
A conjugate prior for discrete hierarchical log-linear models
In Bayesian analysis of multi-way contingency tables, the selection of a
prior distribution for either the log-linear parameters or the cell
probabilities parameters is a major challenge. In this paper, we define a
flexible family of conjugate priors for the wide class of discrete hierarchical
log-linear models, which includes the class of graphical models. These priors
are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear
parameters subject to "baseline constraints" under multinomial sampling. We
also derive the induced prior on the cell probabilities and show that the
induced prior is a generalization of the hyper Dirichlet prior. We show that
this prior has several desirable properties and illustrate its usefulness by
identifying the most probable decomposable, graphical and hierarchical
log-linear models for a six-way contingency table.Comment: Published in at http://dx.doi.org/10.1214/08-AOS669 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Relational models for contingency tables
The paper considers general multiplicative models for complete and incomplete
contingency tables that generalize log-linear and several other models and are
entirely coordinate free. Sufficient conditions of the existence of maximum
likelihood estimates under these models are given, and it is shown that the
usual equivalence between multinomial and Poisson likelihoods holds if and only
if an overall effect is present in the model. If such an effect is not assumed,
the model becomes a curved exponential family and a related mixed
parameterization is given that relies on non-homogeneous odds ratios. Several
examples are presented to illustrate the properties and use of such models
Restricted Covariance Priors with Applications in Spatial Statistics
We present a Bayesian model for area-level count data that uses Gaussian
random effects with a novel type of G-Wishart prior on the inverse
variance--covariance matrix. Specifically, we introduce a new distribution
called the truncated G-Wishart distribution that has support over precision
matrices that lead to positive associations between the random effects of
neighboring regions while preserving conditional independence of
non-neighboring regions. We describe Markov chain Monte Carlo sampling
algorithms for the truncated G-Wishart prior in a disease mapping context and
compare our results to Bayesian hierarchical models based on intrinsic
autoregression priors. A simulation study illustrates that using the truncated
G-Wishart prior improves over the intrinsic autoregressive priors when there
are discontinuities in the disease risk surface. The new model is applied to an
analysis of cancer incidence data in Washington State.Comment: Published at http://dx.doi.org/10.1214/14-BA927 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Modeling uncertainty in macroeconomic growth determinants using Gaussian graphical models
Model uncertainty has become a central focus of policy discussion surrounding the determinants of economic growth. Over 140 regressors have been employed in growth empirics due to the proliferation of several new growth theories in the past two decades. Recently Bayesian model averaging (BMA) has been employed to address model uncertainty and to provide clear policy implications by identifying robust growth determinants. The BMA approaches were, however, limited to linear regression models that abstract from possible dependencies embedded in the covariance structures of growth determinants. The recent empirical growth literature has developed jointness measures to highlight such dependencies. We address model uncertainty and covariate dependencies in a comprehensive Bayesian framework that allows for structural learning in linear regressions and Gaussian graphical models. A common prior specification across the entire comprehensive framework provides consistency. Gaussian graphical models allow for a principled analysis of dependency structures, which allows us to generate a much more parsimonious set of fundamental growth determinants. Our empirics are based on a prominent growth dataset with 41 potential economic factors that has been the utilized in numerous previous analyses to account for model uncertainty as well as jointness.
Copula Gaussian graphical models and their application to modeling functional disability data
We propose a comprehensive Bayesian approach for graphical model
determination in observational studies that can accommodate binary, ordinal or
continuous variables simultaneously. Our new models are called copula Gaussian
graphical models (CGGMs) and embed graphical model selection inside a
semiparametric Gaussian copula. The domain of applicability of our methods is
very broad and encompasses many studies from social science and economics. We
illustrate the use of the copula Gaussian graphical models in the analysis of a
16-dimensional functional disability contingency table.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS397 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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