import Prelude 
import Control.Monad.Bayes.Class
import Control.Monad.Bayes.Enumerator
import Control.Monad.Bayes.Weighted
import Control.Monad.Bayes.Sampler.Strict
import Control.Monad
import Numeric.Log

:l ../plotting.hs

Distributions over anything

In Monad-Bayes, you can have distributions over absolutely any kind of value, of any type. Below, you can see a distribution over histograms, and a distribution over plots.

unnormalizedDistribution :: Measure Double
unnormalizedDistribution = do
    x <- bernoulli 0.5
    y <- normal (if x then (-2) else 2) 1
    factor (normalPdf 0 4 y)
    return y
    
distributionOverWeightedSamples :: Distribution (Double, Log Double)
distributionOverWeightedSamples = weighted unnormalizedDistribution
    
iidDistribution :: Distribution [(Double, Log Double)]
iidDistribution = replicateM 100000 distributionOverWeightedSamples
    
histogramDistribution :: Distribution Histogram
histogramDistribution = histogram 500 <$> iidDistribution
    
plotDistribution :: Distribution Plot
plotDistribution = plot . histogramToList <$> histogramDistribution

unnormalizedDistribution is an (unnormalized) distribution that we want to plot.

distributionOverWeightedSamples is a distribution over pairs of samples from unnormalizedDistribution and their density.

iidDistribution is a distribution over 100000 iid draws from distributionOverWeightedSamples.

histogramDistribution is a distribution over histograms, each corresponding to a possible list of iid samples.

plotDistribution is a distribution over plots (i.e. 2D visualizations that can be rendered in a notebook), each corresponding to a possible histogram.

sampler plotDistribution