The Reference Prior for Complex Covariance Matrices With Efficient Implementation Strategies

Abstract

The paper derives the reference prior for complex covariance matrices. The reference prior is a noninformative prior that circumvents some of the weaknesses of common alternatives in multidimensional settings. As a consequence, inference based on this prior renders well-behaving solutions that in many cases outperform traditionally used approaches. The main obstacle is that inference based on this prior require integration over high-dimensional spaces which have no closed form solutions. A focus of the paper is therefore to discuss efficient implementation strategies based on Markov chain Monte Carlo methods. It is identified that certain structures can be treated analytically both for the case where the parameter of interest is the covariance matrix itself but also for cases in which the covariance matrix is a nuisance parameter that characterizes noise color. Evaluation in both these settings also verify the superior performance obtained by using the proposed prior as compared to traditional techniques to treat unknown covariance matrices.