A PROBABILISTIC LANGUAGE BASED ON SAMPLING FUNCTIONS

Abstract

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This article presents a probabilistic language, called lambda(circle), whose expressive power is beyond discrete distributions. Rich expressiveness of lambda(circle) is due to its use of sampling functions, that is, mappings from the unit interval ( 0.0, 1.0] to probability domains, in specifying probability distributions. As such, lambda(circle) enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of lambda(circle) is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.