General Setup
Estimate a general bivariate polynomial
for some
and
The quality of the estimation will be based on squared-error loss:
We use a Bayesian design
Assume Beta Priors and Posteriors, denoted
and
The Bayes Estimate is just the Posterior Mean:
Goal:
Choose a nonprescient allocation rule
that minimizes the Bayes Risk:
Previous Work
Outline
Example
and
and 
that
minimizes the Bayes Risk:
Previous Work
Outline
Example