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Stochastic Lambda Calculus and Monads of Probability Distributions. Norman Ramsey and Avi Pfeffer. Conference Record of the 29th Annual ACM Symposium on Principles of Programming Languages (POPL'02), in SIGPLAN Notices 37(1):154--165.
Probability distributions form a monad, and the monadic definition leads to a simple, natural semantics for a stochastic lambda calculus, as well as simple, clean implementations of common queries. But the monadic implementation of the expectation query can be much less efficient than current best practices in probabilistic modeling. We therefore present a language of measure terms, which can not only denote discrete probability distributions but can also support the best known modeling techniques.
Some math background is needed for this paper, esp. measure theory.
QuickCheck which was mentioned here a few days ago may serve as a good introduction to some of the ideas analyzed in this paper, since it also discusses probabalistic monads.
It would be very interesting to see the results of the authors promise to investigate Bayesian learning using a monadic framework.
It has been a while since we mentioned probabilistic languages, but this is a fascinating subject. If you have interesting links about such languages, please share!
Posted to LC by Ehud Lamm on 12/30/02; 3:01:00 PM
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Stochastic Lambda Calculus
