The problem of estimation within the matrix variate elliptical model is addressed. In
this paper a subjective Bayesian approach is followed to derive new estimators for the parameters
of the matrix variate elliptical model by assuming the previously intractable normal-Wishart prior.
These new estimators are compared to the estimators derived under a normal-inverse Wishart prior
as well as the objective Jeffreys’ prior which results in the maximum likelihood estimators, using
different measures. A valuable contribution is the development of algorithms for the simulation
of the posterior distributions of the matrix variate parameters with emphasis on the new proposed
estimators. A simulation study as well as Fisher’s Iris data set are used to illustrate the novelty of
these new estimators and to investigate the accuracy gained by assuming the normal-Wishart prior.