Multiparameter Bernoulli factories

Abstract

We consider the problem of computing with many coins of unknown bias. We are given access to samples of n coins with unknown biases p1,…,pn and are asked to sample from a coin with bias f(p1,…,pn) for a given function f:[0,1]n→[0,1]. We give a complete characterization of the functions f for which this is possible. As a consequence, we show how to extend various combinatorial sampling procedures (most notably, the classic Sampford sampling for k-subsets) to the boundary of the hypercube.