Computable Exchangeable Sequences Have Computable de Finetti Measures

Abstract. We prove a uniformly computable version of de Finetti’s theorem on exchangeable sequences of real random variables. In the process, we develop machinery for computably recovering a distribution from its sequence of moments, which suffices to prove the theorem in the case of (almost surely) continuous directing random measures. In the general case, we give a proof inspired by a randomized algorithm which succeeds with probability one. Finally, we show how, as a consequence of the main theorem, exchangeable stochastic processes in probabilistic functional programming languages can be rewritten as procedures that do not use mutation.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Cameron E. Freer, Daniel M. Roy
• Keywords: Applied Computing, CIE 2009, Exchangeable Sequences, Exchangeable Stochastic Processes, Real Random Variables