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# SALib.analyze.delta module

SALib.analyze.delta.analyze(problem: Dict, X: ndarray, Y: ndarray, num_resamples: int = 100, conf_level: float = 0.95, print_to_console: bool = False, seed: int = None, y_resamples: int = None, method: str = 'all') → Dict

  Perform Delta Moment-Independent Analysis on model outputs.

  Returns a dictionary with keys ‘delta’, ‘delta_conf’, ‘S1’, and ‘S1_conf’ (first-order sobol indices), where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file.

  Notes

  Compatible with:

    all samplers

  Examples

      >>> X = latin.sample(problem, 1000)
      >>> Y = Ishigami.evaluate(X)
      >>> Si = delta.analyze(problem, X, Y, print_to_console=True)

  Parameters:

    - problem (dict) – The problem definition

    - X (numpy.matrix) – A NumPy matrix containing the model inputs

    - Y (numpy.array) – A NumPy array containing the model outputs

    - num_resamples (int) – The number of resamples when computing confidence intervals (default 100)

    - conf_level (float) – The confidence interval level (default 0.95)

    - print_to_console (bool) – Print results directly to console (default False)

    - y_resamples (int, optional) – Number of samples to use when resampling (bootstrap) (default None)

    - method ({"all", "delta", "sobol"}, optional) – Whether to compute “delta”, “sobol” or both (“all”) indices (default “all”)

  References

  1. Borgonovo, E. (2007). “A new uncertainty importance measure.”

       Reliability Engineering & System Safety, 92(6):771-784, doi:10.1016/j.ress.2006.04.015.

  2. Plischke, E., E. Borgonovo, and C. L. Smith (2013). “Global

       sensitivity measures from given data.” European Journal of Operational Research, 226(3):536-550, doi:10.1016/j.ejor.2012.11.047.

SALib.analyze.delta.bias_reduced_delta(Y, Ygrid, X, m, num_resamples, conf_level, y_resamples)

  Plischke et al. 2013 bias reduction technique (eqn 30)

SALib.analyze.delta.calc_delta(Y, Ygrid, X, m)

  Plischke et al. (2013) delta index estimator (eqn 26) for d_hat.

SALib.analyze.delta.cli_action(args)

SALib.analyze.delta.cli_parse(parser)

SALib.analyze.delta.sobol_first(Y, X, m)

SALib.analyze.delta.sobol_first_conf(Y, X, m, num_resamples, conf_level, y_resamples)