Bayesian and conditional frequentist analyses of the Fieller's problem. A critical review

摘要: Fieller’s problem belongs to a certain class of problems where there are no methods “objective” inference that viewed as broadly satisfactory (Barbieri et al. 2001; Berger al., 1999). In this paper we analyse the from different viewpoints: frequentist, likelihood and Bayesian. The usual frequentist solution (Fieller, 1954) is considered conditional viewpoint it shown set does not have good properties. We also show analysis fails be operative. On other hand, noninformative Bayesian approach well “calibrated” coverage viewpoint. argue impossible obtain which can both viewpoints. Namely, behaviour very poor, for some value an appropriate conditioning statistic (or set). adopt robust nearly end up with reasonable without introducing prior information on parameters.