RandomMonad

RandomMonad provides a number of composable primitives for constructing "distributions". A distribution is understood in a broad sense: it is anything on which rand can be called. A distribution is like a recipe describing how to construct an object of a certain type. For example, 1:3 is an implicit distribution describing how to pick randomly an Int among 1, 2, 3.

Unlike Distributions.jl which seriously addresses mathematical needs, the RandomMonad package is less specific and is intended to be generally useful for implementing randomness. This is reflected in the core type, a simple Distribution{T}, where T can be anything and is just the type of generated values.

Currently, RandomMonad also implements few classical mathematical distributions, like Bernoulli or Poisson, but these might eventually be split off in another dedicated package.

Examples

A basic distribution is Fill(d, n), defining the generation of arrays of length n of elements drawn from distribution d:

julia> f = Fill(1:9, 4)
Fill(1:9, 4)

julia> eltype(f)
Array{Int64,1}

julia> rand(f)
4-element Array{Int64,1}:
 8
 3
 8
 4

Many algorithms which use randomness can be encapsulated as a distribution. For example, Shuffle defines an alternate API to the Random.shuffle function, but is more general. The following example creates an array of two vectors of length 4 of distinct elements from 1:5:

julia> rand(Fill(Shuffle(1:5), 4), 2)
2-element Array{Array{Int64,1},1}:
 [3, 4, 5, 1]
 [4, 1, 3, 5]

This is sampling from a collection "without replacement", and is equivalent to [StatsBase.sample(1:5, 4, replace=false) for _=1:2].

But... what is a Monad??

I won't add yet another tutorial on monads, but the good news is that knowing the theory of monads is not at all necessary for using this package. It just so happens that Distributions{T} has a monadic structure, and the package provides some related "combinators" (basic blocs to create more elaborate constructions).