flat-mcmc

Painless, efficient, general-purpose sampling from continuous distributions.
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README.md (2000B)

      1 # flat-mcmc
      2 
      3 [![Hackage Version](https://img.shields.io/hackage/v/flat-mcmc.svg)](http://hackage.haskell.org/package/flat-mcmc)
      4 [![MIT License](https://img.shields.io/badge/license-MIT-blue.svg)](https://github.com/jtobin/flat-mcmc/blob/master/LICENSE)
      5 
      6 *flat-mcmc* is a Haskell library for painless, efficient, general-purpose
      7 sampling from continuous distributions.
      8 
      9 *flat-mcmc* uses an ensemble sampler that is invariant to affine
     10 transformations of space.  It wanders a target probability distribution's
     11 parameter space as if it had been "flattened" or "unstretched" in some sense,
     12 allowing many particles to explore it locally and in parallel.
     13 
     14 In general this sampler is useful when you want decent performance without
     15 dealing with any tuning parameters or local proposal distributions.  Check out
     16 the paper describing the algorithm
     17 [here](http://msp.org/camcos/2010/5-1/camcos-v5-n1-p04-p.pdf), and a paper on
     18 some potential limitations [here](http://arxiv.org/abs/1509.02230), authored
     19 by my friends David Huijser and [Brendon
     20 Brewer](https://www.stat.auckland.ac.nz/~brewer/).  There is also also a robust
     21 Python implementation [here](http://dan.iel.fm/emcee/current/) authored by [Dan
     22 Foreman-Mackey](http://dan.iel.fm), a very nice dude who I once moved some
     23 furniture with.
     24 
     25 *flat-mcmc* exports an 'mcmc' function that prints a trace to stdout, as well
     26 as a 'flat' transition operator that can be used more generally.
     27 
     28 ``` haskell
     29 import Numeric.MCMC.Flat
     30 import qualified Data.Vector.Unboxed as U (unsafeIndex)
     31 
     32 rosenbrock :: Particle -> Double
     33 rosenbrock xs = negate (5  * (x1 - x0 ^ 2) ^ 2 + 0.05 * (1 - x0) ^ 2) where
     34   x0 = U.unsafeIndex xs 0
     35   x1 = U.unsafeIndex xs 1
     36 
     37 origin :: Ensemble
     38 origin = ensemble [
     39     particle [negate 1.0, negate 1.0]
     40   , particle [negate 1.0, 1.0]
     41   , particle [1.0, negate 1.0]
     42   , particle [1.0, 1.0]
     43   ]
     44 
     45 main :: IO ()
     46 main = withSystemRandom . asGenIO $ mcmc 12500 origin rosenbrock
     47 ```
     48 
     49 ![trace](http://jtobin.ca/flat-mcmc/img/Rosenbrock_AIE.png)
     50