Abstract

Bayesian and frequentist methodologies when applied to the same model–data information can lead to different statistical inference results. A prominent example involves a rotationally symmetric normal error distribution located at an arbitrary point (θ1,θ2) on the plane. The radial distance ρ = (θ 2 1 + θ2 2)1/2 from the origin has a Bayes posterior survival value s(ρ) that is uniformly greater than the frequentist p-value p(ρ), can be expressed in terms of the noncentral chi-square distribution function with 2 degrees of freedom, and can attain 8 percentage points when ˆρ = 5. We use this Bayes–frequentist difference as a reference to explore the Bayesian bias attributable to parameter curvature. For this, we consider a two parameter regular statistical model and define a curvature measure for an interest parameter; the curvature measure is a mofication of the Efron measure and targets Bayesian adjustment rather than departure from the information lower bound as considered by Efron. Examples are given and simulations are provided.

Citations