Mathilde Bouriga and Olivier Féron have posted a paper on arXiv centred on the estimation of covariance matrices using inverse-Wishart priors. They introduce hyperpriors on the hyperparameters in the spirit of Daniels and Kass (JASA, 1999) and derive Bayes estimators as well as MCMC procedures. They then run a simulation comparison between the different priors in terms of frequentist risks, concluding in favour of the shrinkage covariance estimators that shrink all components of the empirical covariance matrix. (This paper is part of Mathilde’s thesis, which I co-advise with Jean-Michel Marin.)
More among interesting postings on arXiv, many of them published in Statistical Science:
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Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies by Terrance Savitsky, Marina Vannucci, Naijun Sha
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Bayesian Statistical Pragmatism by Andrew Gelman (a discussion of the above)
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A flexible observed factor model with separate dynamics for the factor volatilities and their correlation matrix by Yu-Cheng Ku, Peter Bloomfield, Robert Kohn
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Test martingales, Bayes factors and p-values by Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, Vladimir Vovk
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Pitman-Yor Diffusion Trees by David A. Knowles, Zoubin Ghahramani
