The Multivariate Normal Inverse Gaussian distribution: EM-estimation and analysis of synthetic aperture sonar data

The heavy-tailed Multivariate Normal Inverse Gaussian (MNIG)
distribution is a recent variance-mean mixture of a multivariate
Gaussian with a univariate inverse Gaussian distribution. Due to
the complexity of the likelihood function, parameter estimation
by direct maximization is exceedingly difficult. To overcome this
problem, we propose a fast and accurate multivariate ExpectationMaximization
(EM) algorithm for maximum likelihood estimation
of the scalar, vector, and matrix parameters of the MNIG distribution.
Important fundamental and attractive properties of the MNIG
as a modeling tool for multivariate heavy-tailed processes are discussed.
The modeling strength of the MNIG, and the feasibility of
the proposed EM parameter estimation algorithm, are demonstrated
by fitting the MNIG to real world wideband synthetic aperture sonar
data.