deanie
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jtobin
An embedded probabilistic programming language.
deanie
deanie is an embedded probabilistic programming language. It can be used to denote, sample from, and perform inference on probabilistic programs.
Usage
Programs are written in a straightforward monadic style:
mixture :: Double -> Double -> Program Double
mixture a b = do
p <- beta a b
accept <- bernoulli p
if accept
then gaussian (negate 2) 0.5
else gaussian 2 0.5
You can sample from them by first converting them into an RVar from random-fu:
> sample (rvar (mixture 1 3))
Sample many times from models using standard monadic combinators like 'replicateM':
> replicateM 1000 (sample (rvar (mixture 1 3)))
Or convert them to measures using a built-in interpreter:
> let nu = measure (mixture 1 3)
> let f = cdf nu
You can perform inference on models using rejection or importance sampling, or use a simple, stateful Metropolis backend. Here's a simple beta-bernoulli model, plus some observations to condition on:
betaBernoulli :: Double -> Double -> Program Bool
betaBernoulli a b = do
p <- beta a b
bernoulli p
observations :: [Bool]
observations = [True, True, False, True, False, False, True, True, True]
Here's one way to encode a posterior via rejection sampling:
rposterior :: Double -> Double -> Program Double
rposterior a b =
grejection
(\xs ys -> count xs == count ys)
observations (beta a b) bernoulli
where
count = length . filter id
Here's another, via importance sampling:
iposterior :: Double -> Double -> Program (Double, Double)
iposterior a b =
importance observations (beta a b) logDensityBernoulli
There are also some Monte Carlo convenience functions provided, such as a weighted average for weighted samples returned via importance sampling:
> samples <- replicateM 1000 (sample (rvar (iposterior 1 1)))
> print (mcw samples)
0.6369246537796793
Background
You can read about some of the theory and ideas behind this kind of language in some blog posts I've written.
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