Eaton's Markov chain, its conjugate partner and $\mathscr{P}$-admissibility
Eaton's Markov chain, its conjugate partner and $\mathscr{P}$-admissibility
Suppose that X is a random variable with density $f(x|\theta)$ and that $\pi(\theta|x)$ is a proper posterior corresponding to an improper prior $\nu(\theta)$. The prior is called $\mathscr{P}$-admissible if the generalized Bayes estimator of every bounded function of $\theta$ is almost-$\nu$-admissible under squared error loss. Eaton showed that recurrence of …