Bayesian analysis under ε-contaminated priors: a trade-off between robustness and precision

Optimal Robustness Results for Relative Belief Inferences and the Relationship to Prior-Data Conflict

“…Let γ * (x) = Π Ψ (C Ψ,γ (x) | x) be the exact posterior content of the γ-relative belief region. The following result generalizes results found in Wasserman (1989) and de la Horra and Fernandez (1994) who considered robustness to the prior of credible regions for the full parameter θ. In particular, this result applies to arbitrary parameters ψ = Ψ(θ) and does not require continuity.…”

“…Results in Section 3 establish that these inferences have optimal robustness properties when the marginal prior for ψ is allowed to vary over all possibilities in the class of ǫ-contaminated priors. This generalizes results found in Wasserman (1989), Ruggeri and Wasserman (1993) and de la Horra and Fernandez (1994). Furthermore, an ambiguity concerning the interpretation of the results is resolved.…”

Robust Bayesian Estimation in the One-Dimensional Normal Model

“…the estimator which has the smallest oscillation of the posterior risk under the prior running over a class Γ. Such an approach was presented by Mçczarski and Zielinski [8], Mçczarski [7], de la Horra and Fernandez [6]. We examine the properties of the Bayes estimator, we find the most robust one and we restrict it by some reasonable conditions to avoid too much loss in the quality of estimation.…”