SALib.sample.saltelli module#

SALib.sample.saltelli.cli_action(args)[source]#

Run sampling method

Parameters:

args (argparse namespace)

SALib.sample.saltelli.cli_parse(parser)[source]#

Add method specific options to CLI parser.

Parameters:

parser (argparse object)

Return type:

Updated argparse object

SALib.sample.saltelli.sample(problem: Dict, N: int, calc_second_order: bool = True, skip_values: int = None)[source]#

Generates model inputs using Saltelli’s extension of the Sobol’ sequence

The Sobol’ sequence is a popular quasi-random low-discrepancy sequence used to generate uniform samples of parameter space.

Returns a NumPy matrix containing the model inputs using Saltelli’s sampling scheme.

Saltelli’s scheme extends the Sobol’ sequence in a way to reduce the error rates in the resulting sensitivity index calculations. If calc_second_order is False, the resulting matrix has N * (D + 2) rows, where D is the number of parameters. If calc_second_order is True, the resulting matrix has N * (2D + 2) rows. These model inputs are intended to be used with SALib.analyze.sobol.analyze().

Deprecated since version 1.4.6.

Notes

The initial points of the Sobol’ sequence has some repetition (see Table 2 in Campolongo [1]), which can be avoided by setting the skip_values parameter. Skipping values reportedly improves the uniformity of samples. It has been shown that naively skipping values may reduce accuracy, increasing the number of samples needed to achieve convergence (see Owen [2]).

A recommendation adopted here is that both skip_values and N be a power of 2, where N is the desired number of samples (see [2] and discussion in [5] for further context). It is also suggested therein that skip_values >= N.

The method now defaults to setting skip_values to a power of two that is >= N. If skip_values is provided, the method now raises a UserWarning in cases where sample sizes may be sub-optimal according to the recommendation above.

Parameters:

  • problem (dict) – The problem definition

  • N (int) – The number of samples to generate. Ideally a power of 2 and <= skip_values.

  • calc_second_order (bool) – Calculate second-order sensitivities (default True)

  • skip_values (int or None) – Number of points in Sobol’ sequence to skip, ideally a value of base 2 (default: a power of 2 >= N, or 16; whichever is greater)

References

  1. Campolongo, F., Saltelli, A., Cariboni, J., 2011.

    From screening to quantitative sensitivity analysis. A unified approach. Computer Physics Communications 182, 978-988. https://doi.org/10.1016/j.cpc.2010.12.039

  2. Owen, A. B., 2020.

    On dropping the first Sobol’ point. arXiv:2008.08051 [cs, math, stat]. Available at: http://arxiv.org/abs/2008.08051 (Accessed: 20 April 2021).

  3. Saltelli, A., 2002.

    Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications 145, 280-297. https://doi.org/10.1016/S0010-4655(02)00280-1

  4. Sobol’, I.M., 2001.

    Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, The Second IMACS Seminar on Monte Carlo Methods 55, 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6

  5. Discussion: scipy/scipy#10844

    scipy/scipy#10844 scipy/scipy#10844