
The exact form of the 'Ockham factor' in model selection
We unify the Bayesian and Frequentist justifications for model selection...
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Reconciling the Bayes Factor and Likelihood Ratio for Two NonNested Model Selection Problems
In statistics, there are a variety of methods for performing model selec...
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Bayesian model selection approach for colored graphical Gaussian models
We consider a class of colored graphical Gaussian models obtained by pla...
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Revisiting High Dimensional Bayesian Model Selection for Gaussian Regression
Model selection for regression problems with an increasing number of cov...
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Mean Shrinkage Estimation for HighDimensional Diagonal Natural Exponential Families
Shrinkage estimators have been studied widely in statistics and have pro...
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Bayesian Evidence and Model Selection
In this paper we review the concepts of Bayesian evidence and Bayes fact...
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Quantifying the weight of fingerprint evidence using an ROCbased Approximate Bayesian Computation algorithm
The Bayes factor has been advocated to quantify the weight of forensic e...
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Occam Factor for Gaussian Models With Unknown Variance Structure
We discuss model selection to determine whether the variancecovariance matrix of a multivariate Gaussian model with known mean should be considered to be a constant diagonal, a nonconstant diagonal, or an arbitrary positive definite matrix. Of particular interest is the relationship between Bayesian evidence and the flexibility penalty due to Priebe and Rougier. For the case of an exponential family in canonical form equipped with a conjugate prior for the canonical parameter, flexibility may be exactly decomposed into the usual BIC likelihood penalty and a O_p(1) term, the latter of which we explicitly compute. We also investigate the asymptotics of Bayes factors for linearly nested canonical exponential families equipped with conjugate priors; in particular, we find the exact rates at which Bayes factors correctly diverge in favor of the correct model: linearly and logarithmically in the number of observations when the full and nested models are true, respectively. Such theoretical considerations for the general case permit us to fully express the asymptotic behavior of flexibility and Bayes factors for the variancecovariance structure selection problem when we assume that the prior for the model precision is a member of the gamma/Wishart family of distributions or is uninformative. Simulations demonstrate evidence's immediate and superior performance in model selection compared to approximate criteria such as the BIC. We extend the framework to the multivariate Gaussian linear model with three datadriven examples.
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