When is Eaton’s Markov chain irreducible?
نویسنده
چکیده
Consider a parametric statistical model P (dx|θ) and an improper prior distribution ν(dθ) that together yield a (proper) formal posterior distribution Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [Ann. Statist. 20 (1992) 1147–1179] has shown that a sufficient condition for strong admissibility of ν is the local recurrence of the Markov chain whose transition function is R(θ,dη) = ∫
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