ExpectationProblem

ExpectationProblem(S, g, h, pdist, params)
ExpectationProblem(g, pdist, params)
ExpectationProblem(sm::SystemMap, g, h, d)

Defines ∫ g(S(h(x,u0,p)))*f(x)dx

Arguments

Let 𝕏 = uncertainty space, 𝕌 = Initial condition space, ℙ = model parameter space

• S: 𝕌 × ℙ → 𝕌 also known as system map.
• g: 𝕌 × ℙ → ℝⁿᵒᵘᵗ also known as the observables or output function.
• h: 𝕏 × 𝕌 × ℙ → 𝕌 × ℙ also known as covariate function.
• pdf(d,x): 𝕏 → ℝ the uncertainty distribution of the initial states.
• params

SystemMap(prob, args...; kwargs...)

Representation of a system solution map for a given prob::DEProblem. args and kwargs are forwarded to the equation solver.

ProcessNoiseSystemMap(prob, n, args...; kwargs...)

Representation of a system solution map for a given prob::SDEProblem. args and kwargs are forwarded to the equation solver. n is the number of terms in the Kosambi–Karhunen–Loève representation of the process noise.

GenericDistribution(d, ds...)

Defines a generic distribution that just wraps functions for pdf function, rand and bounds. User can use this for define any arbitrary joint pdf. Included b/c Distributions.jl Product method of mixed distributions are type instable.