Parameterize SobolPayload.params with <: Distribution

[lrennels]

mutable struct SobolPayload
    params::Union{OrderedDict{Symbol, <:Any}, Nothing}
    calc_second_order::Bool
    N::Int 

    function SobolPayload(;params= nothing, calc_second_order = false, N = 1000)
        return new(params, calc_second_order, N)
    end
end

The params attribute of SobolPayload above should be parameterized as `Union{OrderedDict{Symbol, <:Distribution}, Nothing}, however this causes an error because params dictionaries such as

        :x2 => Uniform(0.75, 1.25),
        :x3 => LogNormal(20, 4))

seem to have type OrderedDict{Symbol, Any}, causing an error.

[lrennels]

RIch:

It's because the most specific type that all the elements are a subtype of is the parameterized Distribution{Univariate,Continuous}.

If we define, say, EmpiricalDist as a univariate, discrete Distribution, e.g.,

struct EmpiricalDist <: Distribution{Univariate, Discrete}
     foo::Int
end

we get:

Dict(:a => EmpiricalDistribution1(1), :b => Normal(1, 0.2))
Dict{Symbol,Distribution{Univariate,S} where S<:ValueSupport} with 2 entries:
  :a => EmpiricalDistribution1(foo=1)
  :b => Normal{Float64}(μ=1.0, σ=0.2)

This is a general issue in Julia: since it types a container based on the tightest type that contains all the contents, if your initial values aren't as general as the full set the container will hold, you have to type it explicitly, or the later additions (that fall outside the narrow type) will fail.

So, yes,

params = OrderedDict{Symbol, Distribution}(:x1 => Normal(1, 0.2),
        :x2 => Uniform(0.75, 1.25),
        :x3 => LogNormal(20, 4))

is the way to go.

[lrennels]

Need to decide if this is worth it, because don't want user to have to parameterize their input so specifically.