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Generate a Sobol Design for Parameter Exploration

Source: R/sobol_design.R
sobol_design.Rd

Creates a Latin hypercube design based on the Sobol low-discrepancy sequence. This function provides an API-compatible alternative to the sobol_design function in the pomp-explore package for generating parameter designs.

Usage

sobol_design(lower = numeric(0), upper = numeric(0), nseq)

Arguments

lower

Named numeric vector giving the lower bounds of the parameter ranges. Must have the same names as upper.

upper

Named numeric vector giving the upper bounds of the parameter ranges. Must have the same names as lower.

nseq

Integer, the total number of parameter sets (points) to generate.

Value

A data frame with nseq rows and one column for each parameter named in lower and upper. Each column contains values scaled to the specified range [lower, upper] for that parameter.

Details

This function generates a Sobol sequence in the unit hypercube [0,1]^d and then scales each dimension to the specified parameter ranges. The Sobol sequence is generated using the Joe-Kuo direction numbers with Property A enforcement, providing excellent low-discrepancy properties.

Following the recommendation of Joe & Kuo (2003) and the implementation in pomp-explore, this function skips the first k points of the Sobol sequence, where k is the largest power of 2 smaller than nseq. This improves the uniformity properties of the generated design.

The function is designed to be API-compatible with the sobol_design function from the pomp-explore package, allowing for easy comparison and drop-in replacement.

References

Bratley, P., & Fox, B. L. (1988). Algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Transactions on Mathematical Software, 14(1), 88-100.

Joe, S., & Kuo, F. Y. (2008). Constructing Sobol sequences with better two-dimensional projections. SIAM Journal on Scientific Computing, 30(5), 2635-2654.

See also

sobol_points for batch generation without scaling, sobol_generator for incremental generation

Examples

# Generate 100 parameter sets for two parameters
design <- sobol_design(
  lower = c(a = 0, b = 100),
  upper = c(a = 1, b = 200),
  nseq = 100
)
head(design)
#>           a        b
#> 1 0.0234375 182.0312
#> 2 0.5234375 132.0312
#> 3 0.7734375 157.0312
#> 4 0.2734375 107.0312
#> 5 0.3984375 144.5312
#> 6 0.8984375 194.5312

# Plot the design
plot(design$a, design$b, main = "Sobol Design")


# High-dimensional example
params <- paste0("param", 1:10)
design_10d <- sobol_design(
  lower = setNames(rep(0, 10), params),
  upper = setNames(rep(1, 10), params),
  nseq = 1000
)