The Extraction of Information From Multiple Point Estimates

The use of a number of point estimation experiments to construct a least informative prior subject to the information in the estimation experiments is studied. The form of the resulting prior is established. The prior depends on parameters that result from solving a calculus of variations problem. It is shown that simple Gibbs sampler algorithms converge to the desired solution, and simulated annealing algorithms yield the mode of the prior. The Gibbs sampler algorithm is ergodic, and hence Bayes risks can be directly computed using time averages of a single series of draws from the sampler.