Unlike all the other layers, all the subdomains of the Probability layer share the same enabling type Dist, the only thing differing being the numerical recipe to obtain a distributed value.

To make full advantage of Haskell's lazyness and its native libraries for random number generation (e.g. System.Random) we represent recipes in the most generic form as functions \(\mathbf{1}\rightarrow[\alpha]\) from a seed (here StdGen) to an infinite list containing all possible values in a random sequence. Any practical simulation/tracing thus needs to limit this list to a finite number of experiments.

The map atom. It lifts an abitrary function \(f\) from a layer below and creates a random variable \(\mathbf{y}=f(\mathbf{x})\) by mapping every point from the original random variable according to \(f\).

The applicative atom. Transforms one random variable distribution to another by mapping samples.

Returns all possible values of a random variable as an infinite list of values.

Samples a random variable by running one experiment trial defined by a certain distribution.

Samples a random variable by running n experiment trials defined by a certain distribution. This is equivalent to running a Monte Calro experiment on n samples.

This pattern transforms a (set of) random distribution(s) into another (set) by composing their recipes with an arbitrary function. In other words it lifts an arbitrary function to the Probability layer.

Constructors: trans[1-8][1-4]

Histogram representation as a zipped list of bins, each bin paired with its center value.

Returns the histogram of (a list of) experiments.

>>> let xs = [1..10] ++ [4..7]
>>> histogram 1 10 2 xs
{(1.0,1) (3.0,2) (5.0,4) (7.0,4) (9.0,2)}