Maximum A Posteriori Covariance Estimation Using a Power Inverse Wishart Prior

The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is large compared to the number of samples, and the usual maximum likelihood estimate is poor. Typically, improvements are obtained by modelling or regularization. From a practical point of view, these methods are often computationally heavy and rely on approximations. As a fast substitute, we propose an easily calculable maximum a posteriori (MAP) estimator based on a new class of prior distributions generalizing the inverse Wishart prior, discuss its properties, and demonstrate the estimator on simulated and real data.