Sampling function-based probability distributions.

A simple probability distribution type, where distributions are characterized by sampling functions.

This implementation is a thin layer over mwc-random, which handles RNG state-passing automatically by using a PrimMonad like IO or ST s under the hood.

Examples

Transform a distribution's support while leaving its density structure invariant:

-- uniform over [0, 1] to uniform over [1, 2]
fmap succ uniform

Sequence distributions together using bind:

-- a beta-binomial compound distribution
beta 1 10 >>= binomial 10

Use do-notation to build complex joint distributions from composable, local conditionals:

hierarchicalModel = do
  [c, d, e, f] <- replicateM 4 $ uniformR (1, 10)
  a <- gamma c d
  b <- gamma e f
  p <- beta a b
  n <- uniformR (5, 10)
  binomial n p

mwc-probability

Sampling function-based probability distributions.

A simple probability distribution type, where distributions are characterized by sampling functions.

This implementation is a thin layer over mwc-random, which handles RNG state-passing automatically by using a PrimMonad like IO or ST s under the hood.

Examples

• Transform a distribution's support while leaving its density structure invariant:

  -- uniform over [0, 1] transformed to uniform over [1, 2]
  succ <$> uniform
  

• Sequence distributions together using bind:

  -- a beta-binomial composite distribution
  beta 1 10 >>= binomial 10
  

• Use do-notation to build complex joint distributions from composable, local conditionals:

  hierarchicalModel = do
    [c, d, e, f] <- replicateM 4 (uniformR (1, 10))
    a <- gamma c d
    b <- gamma e f
    p <- beta a b
    n <- uniformR (5, 10)
    binomial n p
  

Check out the haddock-generated docs on Hackage for other examples.

Etc.

PRs and issues welcome.