Estimation of covariance matrices
Mathilde Bouriga and Olivier Féron have posted a paper on arXiv centred on the estimation of covariance matrices using inverseWishart 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 coadvise with JeanMichel Marin.)
More among interesting postings on arXiv, many of them published in Statistical Science:

Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies by Terrance Savitsky, Marina Vannucci, Naijun Sha

Bayesian Statistical Pragmatism by Andrew Gelman (a discussion of the above)

A flexible observed factor model with separate dynamics for the factor volatilities and their correlation matrix by YuCheng Ku, Peter Bloomfield, Robert Kohn

Test martingales, Bayes factors and pvalues by Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, Vladimir Vovk

PitmanYor Diffusion Trees by David A. Knowles, Zoubin Ghahramani
June 22, 2011 at 9:38 am
Quantitative geneticists have been estimating (genetic) covariance matrices for decades and been confronted to this problem. A recent paper that suggests shrunken estimators is here
http://www.genetics.org/content/185/3/1097
and references therein.
June 21, 2011 at 2:03 am
I’m struggling with the model in “Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies”…
As far as I can see, they’re modelling relationships between *covariates* using a GP prior. This necessitates a ‘closeness’ in covariate space that is really hard for me to get my head around – what is the metric between wind speed and the GDP of Kenya? Even if there is a ‘closeness’, the variable selection model doesn’t make sense under ‘infill’ conditions.
Am I missing something?
June 21, 2011 at 6:59 am
Dan: I have not read the paper yet… This is an incentive for doing so!