Affine Monads and Lazy Structures for Bayesian Programming
summary
Argues that infinite-dimensional Bayesian models (Poisson, Gaussian, Dirichlet, Beta, jump processes) are naturally expressed with lazy streams and infinite trees, and that semantics require two distinct monads: an affine probability monad for lazy sampling and a non-affine measures monad for scoring. Proves decidability/semantic separation using quasi-Borel spaces, gives Metropolis-Hastings-Green–based correctness for new lazy-aware inference moves, implements two Monte Carlo algorithms plus LazyPPL in Haskell using infinite random-seed trees and stochastic memoization.
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chapters (5)
- 0:00Start
- 0:35Probabilistic programming with lazy infinite structures • A language for building distributions and measures • Complex non-parametric models (infinite or unbounded dimension): lazy programming is natural
- 4:28Example: random piecewise functions
- 6:45The metalanguage (Prob)
- 12:44The metalanguage (Prob + Meas) Add a monad Meas of un-normalized measures
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