  Construction methods for prior densities are investigated from a predictive
viewpoint. Predictive densities for future observables are constructed by using
observed data. The simultaneous distribution of future observables and observed
data is assumed to belong to a parametric submodel of a multinomial model.
Future observables and data are possibly dependent. The discrepancy of a
predictive density to the true conditional density of future observables given
observed data is evaluated by the Kullback-Leibler divergence. It is proved
that limits of Bayesian predictive densities form an essentially complete
class. Latent information priors are defined as priors maximizing the
conditional mutual information between the parameter and the future observables
given the observed data. Minimax predictive densities are constructed as limits
of Bayesian predictive densities based on prior sequences converging to the
latent information priors.
