Suppose that X is a random variable with density f(xj ) and that ( jx) is a proper posterior corresponding to an improper prior ( ). The prior is called P-admissible if the generalized Bayes estimator of every bounded function of is almost-admissible under squared error loss. Eaton (1992) showed that recurrence of the Markov chain with transition density R( j ) = R ( jx)f(xj )dx is a su cient condition for P-admissibility of ( ). We show that Eaton's Markov chain is recurrent if and only if its… CONTINUE READING