Implement Design module wrapping QuasiMonteCarlo.jl + GlobalSensitivity.jl

[jc-macdonald]

Summary

Port design.py for experimental design: full factorial grids, LHS/QMC sampling, and sensitivity screening.

Functions to Implement

Function	Description	Julia dep
build_grid(factors; method=:full)	Full factorial grid	Combinatorics / custom iterator
build_grid(factors; method=:lhs, n=...)	Latin Hypercube / QMC	QuasiMonteCarlo.jl
build_grid(factors; method=:sobol, n=...)	Sobol QMC sequence	QuasiMonteCarlo.jl
screen(factors, model; method=:morris)	Morris OAT sensitivity screening	GlobalSensitivity.jl
reduce_factors(screening_result; threshold)	Drop insensitive factors	Pure Julia

Types to Implement

@enum FactorType CONTINUOUS DISCRETE CATEGORICAL

struct Factor
    name::Symbol
    type::FactorType
    levels  # Vector for CATEGORICAL/DISCRETE, Tuple{Float64,Float64} for CONTINUOUS
end

Design Notes

• QuasiMonteCarlo.jl (SciML) provides LHS, Sobol, Halton, Faure, lattice rules + scrambling. Superior to LatinHypercubeSampling.jl (unmaintained since 2023).
• GlobalSensitivity.jl (SciML, JOSS published) supports Sobol, Morris, eFAST, DGSM, PAWN, RBD-FAST — exceeds SALib's coverage.
• Full factorial for discrete/categorical factors: use Iterators.product from Base.

Dependencies

[deps]
QuasiMonteCarlo = "..."
GlobalSensitivity = "..."

[compat]
QuasiMonteCarlo = "0.3"
GlobalSensitivity = "2"

Acceptance Criteria

• Full factorial matches expected row count
• LHS produces correct dimensionality and bounds
• Morris screening identifies known-sensitive factors in test function
• Continuous + categorical factors handled in mixed designs