README.md (2932B)

1 2 # deanie 3 4 [![MIT License](https://img.shields.io/badge/license-MIT-blue.svg)](https://github.com/jtobin/deanie/blob/master/LICENSE) 5 6 *deanie* is an embedded probabilistic programming language. It can be used to 7 denote, sample from, and perform inference on probabilistic programs. 8 9 ## Usage 10 11 Programs are written in a straightforward monadic style: 12 13 ``` haskell 14 mixture :: Double -> Double -> Program Double 15 mixture a b = do 16 p <- beta a b 17 accept <- bernoulli p 18 if accept 19 then gaussian (negate 2) 0.5 20 else gaussian 2 0.5 21 ``` 22 23 You can sample from them by first converting them into an *RVar* from 24 [random-fu][rafu]: 25 26 ``` 27 > sample (rvar (mixture 1 3)) 28 ``` 29 30 Sample many times from models using standard monadic combinators like 31 'replicateM': 32 33 ``` 34 > replicateM 1000 (sample (rvar (mixture 1 3))) 35 ``` 36 37 ![](assets/mixture.png) 38 39 Or convert them to measures using a built-in interpreter: 40 41 ``` 42 > let nu = measure (mixture 1 3) 43 > let f = cdf nu 44 ``` 45 46 ![](assets/mixture_cdf.png) 47 48 You can perform inference on models using rejection or importance sampling, or 49 use a simple, stateful Metropolis backend. Here's a simple beta-bernoulli 50 model, plus some observations to condition on: 51 52 ``` haskell 53 betaBernoulli :: Double -> Double -> Program Bool 54 betaBernoulli a b = do 55 p <- beta a b 56 bernoulli p 57 58 observations :: [Bool] 59 observations = [True, True, False, True, False, False, True, True, True] 60 ``` 61 62 Here's one way to encode a posterior via rejection sampling: 63 64 ``` haskell 65 rposterior :: Double -> Double -> Program Double 66 rposterior a b = 67 grejection 68 (\xs ys -> count xs == count ys) 69 observations (beta a b) bernoulli 70 where 71 count = length . filter id 72 ``` 73 74 ![](assets/bb_rejection.png) 75 76 Here's another, via importance sampling: 77 78 ``` haskell 79 iposterior :: Double -> Double -> Program (Double, Double) 80 iposterior a b = 81 importance observations (beta a b) logDensityBernoulli 82 ``` 83 84 There are also some Monte Carlo convenience functions provided, such as a 85 weighted average for weighted samples returned via importance sampling: 86 87 ``` 88 > samples <- replicateM 1000 (sample (rvar (iposterior 1 1))) 89 > print (mcw samples) 90 0.6369246537796793 91 ``` 92 93 ## Background 94 95 You can read about some of the theory and ideas behind this kind of language in 96 some blog posts I've written. 97 98 * [Encoding Statistical Independence, Statically][enco] 99 * [A Simple Embedded Probabilistic Programming Language][sppl] 100 * [Comonadic MCMC][como] 101 * [Foundations of the Giry Monad][gifo] 102 * [Implementing the Giry Monad][gimp] 103 * [The Applicative Structure of the Giry Monad][giap] 104 105 [giap]: https://jtobin.io/giry-monad-applicative 106 [gimp]: https://jtobin.io/giry-monad-implementation 107 [gifo]: https://jtobin.io/giry-monad-foundations 108 [enco]: https://jtobin.io/encoding-independence-statically 109 [sppl]: https://jtobin.io/simple-probabilistic-programming 110 [como]: https://jtobin.io/comonadic-mcmc 111 [rafu]: https://hackage.haskell.org/package/random-fu 112