Belief function and multivalued mapping robustness in statistical estimation

• We consider robust inference problems in which the prior and/or likelihood are modelled by belief functions.
• We derive inference by using the multivalued mapping interpretation of belief functions.
• We exploit mathematical tools from Walleyʼs theory of imprecise probabilities.
• We apply the derived robust models to practical inference problems.
• We show the connections of the proposed inference method with interval estimation and statistical inference with missing data.

We consider the case in which the available knowledge does not allow to specify a precise probabilistic model for the prior and/or likelihood in statistical estimation. We assume that this imprecision can be represented by belief functions models. Thus, we exploit the mathematical structure of belief functions and their equivalent representation in terms of closed convex sets of probabilities to derive robust posterior inferences using Walleyʼs theory of imprecise probabilities. Then, we apply these robust models to practical inference problems and we show the connections of the proposed inference method with interval estimation and statistical inference with missing data.