On Simulating a Class of Bernstein Polynomials
Given a black box that generates independent Bernoulli samples with an unknown bias p, we consider the problem of simulating a Bernoulli random variable with bias f(p) (where f is a given function) using a finite (computable in advance) number of independent Bernoulli samples from the black box. We show that this is possible if and only if f is a Bernstein polynomial with coefficients between 0 and 1, and we explicitly give the algorithm. Our results differ from Keane and O'Brien [1994] in that our goal is more modest/stringent, since we are considering algorithms that use a finite number of samples as opposed to allowing a random number (such as in acceptance rejection algorithms).
simulation bernstein polynomials