Parameter estimation with a class of outer probability measures

01/02/2018

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by   Jeremie Houssineau, et al.

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We explore the interplay between random and deterministic phenomena using a novel representation of uncertainty. The proposed framework strengthens the connections between the frequentist and Bayesian approaches by allowing for the two viewpoints to coexist within a unified formulation. The meaning of the analogues of different probabilistic concepts is investigated and examples of application are provided in a variety of statistical topics such as information theory, maximum likelihood estimation, model selection, Markov chain theory and point process theory.