vars_to {sensobol}

Computation of VARS Total order index (VARS-TO)

Description

It computes VARS-TO following Razavi and Gupta (2016).

Usage

vars_to(Y, star.centers, params, h, method = "all.step")

Arguments

Y

A numeric vector with the model output obtained from the matrix created with vars_matrices.

star.centers

Positive integer, number of star centers.

params

Character vector with the name of the model inputs.

h

Distance between pairs.

method

Type of computation. If method = "all.step", all pairs of points with values \Delta h, 2\Delta h, 3\Delta h,... are used in each dimension. If method = "one.step", only the pairs \Delta h away are used. The default is method = "all.step".

Details

VARS is based on variogram analysis to characterize the spatial structure and variability of a given model output across the input space (Razavi and Gupta 2016). Variance- based total-order effects can be computed as by-products of the VARS framework. The total-order index is related to the variogram \gamma(.) and co-variogram C(.) functions by the following equation:

T_i = \frac{\gamma (h_i) + E \left [C_{\mathbf{x}_{\sim i}} (h_i) \right]}{\hat{V}(y)}

where x^*_{\sim i} is a vector of all k factors except x_i.

Value

A data.table with the VARS-TO indices of each parameter.

References

Razavi S, Gupta HV (2016). “A new framework for comprehensive, robust, and efficient global sensitivity analysis: 2. Application.” Water Resources Research, 52(1), 440–455. doi:10.1002/2015WR017558, 2014WR016527.

Examples

# Define settings
star.centers <- 10; params <- paste("X", 1:3, sep = ""); h <- 0.1

# Create STAR-VARS
mat <- vars_matrices(star.centers = star.centers, params = params, h = h)

# Run model
y <- sensobol::ishigami_Fun(mat)

# Compute VARS-TO
ind <- vars_to(Y = y, star.centers = star.centers, params = params, h = h)
ind