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In conventional hydrothermal synthesis of porous titanosilicate materials, undesired aggregation of TiO2 species during the synthesis limits the content of active four-coordinated Ti to an Si/Ti ratio of about 40....

Summary A Bayesian prediction problem for the two-dimensional Wishart model is investigated within the framework of decision theory. The loss function is the Kullback–Leibler divergence. We construct a scale-invariant and permutation-invariant prior distribution that shrinks the correlation coefficient. The prior is the geometric mean of the right invariant prior with respect to permutation of the indices and is characterized by a uniform distribution for Fisher’s z-transformation of the correlation coefficient. The Bayesian predictive density based on the prior is shown to be minimax.