LazyPPL

LazyPPL is a Haskell library for Bayesian probabilistic programming. It supports lazy use of probability, and we provide new Metropolis-Hastings algorithms to allow this. LazyPPL is inspired by recent ideas in synthetic probability theory and synthetic measure theory, such as quasi-Borel spaces and Markov categories. Laziness appears to be a good paradigm for non-parametric statistics. LazyPPL is inspired by many other languages, including Church, Anglican, and MonadBayes. Several aspects are now incorporated into MonadBayes (see here).

LazyPPL provides two monads:

• Prob a: probability measures, supporting probability measure such as uniform :: Prob Double, normal :: Double -> Double -> Prob Double, bernoulli :: Double -> Prob Bool. This is lazy, in other words it is an affine monad.
• Meas a: unnormalized measures, as used in Monte Carlo simulations for Bayesian statistics. There are two key functions:
  • sample :: Prob a -> Meas a, which samples from a probability measure;
  • score :: Double -> Meas (), which weights a measure by a given value, typically coming from a likelihood function.

Simple example

To illustrate the basic usage, here is a very simple first example, that doesn’t use laziness. More advanced examples are in the menu above, and further examples in the GitHub repository.

{-# LANGUAGE ExtendedDefaultRules #-}
module Index where
import LazyPPL
import Distr
import Graphics.Matplotlib hiding (density)
import Data.List

model :: Meas Bool
model = do
  -- Prior belief: it is Sunday with prob. 1/7
  sunday <- sample $ bernoulli (1/7)
  -- I know the rates of buses on the different days:
  let rate = if sunday then 3 else 10 
  -- observe 4 buses
  score $ poissonPdf rate 4
  return sunday

inference :: IO ()
inference = do
  xws <- mh 1 model
  plotHistogram "images/index-posterior.svg" (map fst $ take 1000 xws)

plotHistogram :: (Show a , Eq a) => String -> [a] -> IO ()
plotHistogram filename xs = do
  putStrLn $ "Generating " ++ filename ++ "..."
  let categories = nub xs
  let counts = map (\c -> length $ filter (==c) xs) categories
  file filename $ bar (map show categories) $ map (\n -> (fromIntegral n)/(fromIntegral $ length xs)) counts
  putStrLn $ "Done."

main = do {inference}