  Shape restricted regressions, including isotonic regression and concave
regression as special cases, are studied using priors on Bernstein polynomials
and Markov chain Monte Carlo methods. These priors have large supports, select
only smooth functions, can easily incorporate geometric information into the
prior, and can be generated without computational difficulty. Algorithms
generating priors and posteriors are proposed, and simulation studies are
conducted to illustrate the performance of this approach. Comparisons with the
density-regression method of Dette et al. (2006) are included.
