James P. Hobert

Department of Statistics

University of Florida

Markov Chain Conditions for Admissibility

Suppose that $X$ is a random vector with density $f(x|\theta)$ and that $\pi(\theta|x)$ is a proper posterior density corresponding to an improper prior $\nu(\theta)$. The prior is called strongly admissible if the formal Bayes estimator of every bounded function of $\theta$ is admissible under squared error loss. Eaton (1992, Annals of Statistics) showed that recurrence of a certain Markov chain, $W$, defined in terms of $f$ and $\nu$, implies the strong admissibility of $\nu$. Hobert and Robert (1999, Annals of Statistics) showed that $W$ is recurrent if and only if a related Markov chain, \tilde{W}$, is recurrent. I will show that when $X$ is an exponential random variable, a fairly thorough analysis of the Markov chain $\tilde{W}$ is possible and this leads to a simple sufficient condition for strong admissibility. I will also explain how the relationship between $W$ and $\tilde{W}$ can be used to establish that certain perturbations of strongly admissible priors retain strong admissibility.

(This is joint work with M. Eaton, G. Jones, D. Marchev and J. Schweinsberg.)

Back to Colloquium Series