On the Representation of Ignorance Regarding a Matrix of Reduced Rank

 by Mattias Villani

 Research Report 1998:11

 Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden


A common feature of many multivariate models is the presence of a coefficient matrix with reduced rank. A Bayesian analysis of such models requires a prior distribution which takes the reduced rank restriction and the necessary normalizations into account. It is shown here that the consequences of ignoring the reduced rank and the use of standard diffuse priors lead to a highly arbitrarily informative prior on the aspects of the model with real meaning. It is well known that only spaces spanned by columns or rows of a reduced rank matrix are determinable. This observation is the foundation on which we suggest new priors for two different definitions of diffuseness and under two different normalizations.

 Key words: Bayesian; Cointegration; Common factor model; Diffuse; Matrix Cauchy; MANOVA; Multivariate; Prior distribution; Reduced rank regression. 

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Last update: 1999-01-27 / MV