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Thursday, May 30
Computational Statistics
Recent Developments in Lower Rank Learning for Complex Data
Thu, May 30, 10:30 AM - 12:05 PM
Grand Ballroom K

Bayesian Analysis of the Covariance Matrix of a Multivariate Normal Distribution with a New Class of Priors (305011)

*Dongchu Sun, University of Missouri 

Keywords: Wishart distribution, shrinkage inverse Wishart distributon, Jeffreys prior, covariance matrix, low rank learning

Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this talk, we propose a new class of priors for the covariance matrix, including both inverse Wishart and reference priors as special cases. The main motivation for the new class is to have available priors -- both subjective and objective -- that do not ``force eigenvalues apart," which is a criticism of inverse Wishart and Jeffreys priors. Extensive comparison of these `shrinkage priors' with inverse Wishart and Jeffreys priors is undertaken, with the new priors seeming to have considerably better performance. A number of curious facts about the new priors are also observed, such as that the posterior distribution will be proper with just three vector observations from the multivariate normal distribution -- regardless of the dimension of the covariance matrix -- and that useful inference about features of the covariance matrix can be possible. Finally, a new MCMC algorithm is developed for this class of priors and is shown to be computationally effective for matrices of up to 100 dimensions.