Space-filling designs

When you attach several variations to a trial, the sampling method decides which combinations of values are actually run. The default enumerates every combination; the space-filling designs sample the parameter space more efficiently for high-dimensional sweeps. The method is the optional first argument to createTrial and run.

All four methods are subtypes of AddVariationMethod.

GridVariation (default)

GridVariation takes the full factorial grid — every combination of every discrete variation's values. With three variations of 3, 4, and 2 values that is 3 × 4 × 2 = 24 monads.

run(GridVariation(), inputs, dv1, dv2)   # or just: run(inputs, dv1, dv2)

Grids are exhaustive and exact, but the count grows multiplicatively — use a space-filling design when the dimension is high.

LHSVariation

LHSVariation draws a Latin Hypercube Sample of size n: each parameter's range is split into n equal-probability bins and sampled so every bin is used exactly once. Good coverage with far fewer points than a grid.

run(LHSVariation(100), inputs, dist1, dist2)
run(LHSVariation(100; add_noise=true, orthogonalize=true), inputs, dist1, dist2)

• add_noise — jitter within each bin instead of using bin centers.
• orthogonalize — use an orthogonal LHS for better space coverage (on by default).

SobolVariation

SobolVariation uses a Sobol low-discrepancy quasi-random sequence — deterministic, highly uniform coverage that is the basis for Sobol' sensitivity analysis.

run(SobolVariation(128), inputs, dist1, dist2)
run(SobolVariation(; pow2=7), inputs, dist1, dist2)   # n = 2^7 = 128

n_matrices, randomization, skip_start, and include_one control the sequence; the pow2 keyword is a convenience for power-of-two sample sizes.

RBDVariation

RBDVariation builds a Random Balance Design, used by RBD-FAST sensitivity analysis. With the default Sobol-based construction, n must be within one of a power of two.

run(RBDVariation(128), inputs, dist1, dist2)
run(RBDVariation(100; use_sobol=false), inputs, dist1, dist2)   # random-sequence variant

Choosing a design

The space-filling methods pair naturally with DistributedVariations, since they sample distributions rather than enumerate fixed values. For analyses built directly on these designs, see Sensitivity analysis. For the result types (AddVariationsResult and its subtypes) and orthogonalLHS, see the Variations & designs API reference.