Imprecise Hierarchical Dirichlet model with applications

Many estimation problems in data fusion involve multiple parameters that can be related in some way by the structure of the problem. This implies that a joint probabilistic model for these parameters should reflect this dependence. In parametric estimation, a Bayesian way to account for this possible dependence is to use hierarchical models, in which data depends on hidden parameters that in turn depend on hyperprior parameters. An issue in this analysis is how to choose the hyperprior in case of lack of prior information. This paper focuses on parametric estimation problems involving multinomial-Dirichlet models and presents a model of prior ignorance for the hyperparameters. This model consists to a set of Dirichlet distributions that expresses a condition of prior ignorance. We analyse the theoretical properties of this model and we apply it to practical fusion problems: (i) the estimate of the packet drop rate in a centralized sensor network; (ii) the estimate of the transition probabilities for a multiple-model algorithm.