Maximum likelihood estimation under order restrictions by the prior feedback method

Algorithms for deriving isotonic regression estimators id order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied ''universally''; that is, as long as these Bayes estimators can be derived by exact computation or Markov chain Monte Carlo sampling approximation. We then give an illustration of our method for two real-life examples.