Type: Package
Title: Sobol Indices for Models with Fixed and Stochastic Parameters
Version: 0.4.0
Date: 2025-11-26
Depends: R (≥ 3.5.0)
Imports: ggplot2, Rcpp (≥ 1.0.0), rlang, sensitivity, stats
Suggests: knitr, markdown, rmarkdown, simmer, testthat (≥ 3.0.0)
LinkingTo: Rcpp
Author: Frederic Bertrand ORCID iD [cre, aut], Elizaveta Logosha [aut], Myriam Maumy-Bertrand ORCID iD [aut]
Maintainer: Frederic Bertrand <frederic.bertrand@lecnam.net>
Description: Tools to design experiments, compute Sobol sensitivity indices, and summarise stochastic responses inspired by the strategy described by Zhu and Sudret (2021) <doi:10.1016/j.ress.2021.107815>. Includes helpers to optimise toy models implemented in C++, visualise indices with uncertainty quantification, and derive reliability-oriented sensitivity measures based on failure probabilities. It is further detailed in Logosha, Maumy and Bertrand (2022) <doi:10.1063/5.0246026> and (2023) <doi:10.1063/5.0246024> or in Bertrand, Logosha and Maumy (2024) https://hal.science/hal-05371803, https://hal.science/hal-05371795 and https://hal.science/hal-05371798.
LazyLoad: yes
VignetteBuilder: knitr
License: GPL-3
Encoding: UTF-8
URL: https://fbertran.github.io/Sobol4R/, https://github.com/fbertran/Sobol4R
BugReports: https://github.com/fbertran/Sobol4R/issues
RoxygenNote: 7.3.3
NeedsCompilation: yes
Packaged: 2025-11-27 00:54:30 UTC; bertran7
Repository: CRAN
Date/Publication: 2025-12-02 15:00:02 UTC

Sobol4R-package

Description

Tools to design experiments, compute Sobol sensitivity indices, and summarise stochastic responses inspired by the strategy described by Zhu and Sudret (2021) doi:10.1016/j.ress.2021.107815. Includes helpers to optimise toy models implemented in C++, visualise indices with uncertainty quantification, and derive reliability-oriented sensitivity measures based on failure probabilities. It is further detailed in Logosha, Maumy and Bertrand (2022) doi:10.1063/5.0246026 and (2023) doi:10.1063/5.0246024 or in Bertrand, Logosha and Maumy (2024) https://hal.science/hal-05371803, https://hal.science/hal-05371795 and https://hal.science/hal-05371798.

Author(s)

Maintainer: Frederic Bertrand frederic.bertrand@lecnam.net (ORCID)

Authors:

References

Elizaveta Logosha, Myriam Maumy, Frederic Bertrand; Confidence interval determination using discrete event simulations for real estate sales case. AIP Conf. Proc. 31 March 2025; 3182 (1): 100008. doi:10.1063/5.0246026.

Elizaveta Logosha, Myriam Maumy, Frédéric Bertrand; Sensitivity analysis of stochastic simulator in the case of sales date prediction. AIP Conf. Proc. 31 March 2025; 3182 (1): 100001. doi:10.1063/5.0246024.

Frédéric Bertrand, Elizaveta Logosha, Myriam Maumy-Bertrand. Extension of sensitivity analysis to uncertainties in distribution parameters. 32nd Conference on Intelligent Systems for Molecular Biology, International Society for Computational Biology, Jul 2024, Montreal (QC), Canada. https://hal.science/hal-05371795.

Frédéric Bertrand, Elizaveta Logosha, Myriam Maumy-Bertrand. Sobol4RV: Global Sensitivity Analysis in Several Random Settings. BioC 2024, BioConductor, Jul 2024, Grand Rapids, MI, United States. https://hal.science/hal-05371803

Frédéric Bertrand, Elizaveta Logosha, Myriam Maumy-Bertrand. Global Sensitivity Analysis in Several Random Settings. 2024 Joint Statistical Meetings, American Statistical Association, Aug 2024, Portland (OR), United States. https://hal.science/hal-05371798.

See Also

sobol4r_design(), sobol4r_qoi_indices(), vignette("Sobol_RV_five_examples", package = "Sobol4R"), vignette("Sobol4R_vignette_stochastic", package = "Sobol4R"), vignette("Sobol4R_vignette_process", package = "Sobol4R") and vignette("simmer_MM1_Sobol_example", package = "Sobol4R").

Examples

ex1_results <- sobol_example_g_deterministic(n=100, nboot=10) 
print(ex1_results)
autoplot(ex1_results, ncol = 1)
rm(ex1_results)

Autoplot implementations

Description

Provide a ggplot visualisation when ggplot2 is available, otherwise fallback to a lightweight base R bar chart. Supports the custom sobol_result class used in this package, compact sobol_summary data frames, and sensitivity::sobol objects.

Usage

autoplot(object, ...)

## S3 method for class 'sobol_result'
autoplot(
  object,
  show_uncertainty = FALSE,
  probs = c(0.1, 0.9),
  bootstrap = 200L,
  ...
)

## S3 method for class 'sobol'
autoplot(object, separate_panels = TRUE, ncol = 2, ...)

## S3 method for class 'sobol2007'
autoplot(object, ...)

## S3 method for class 'soboljansen'
autoplot(object, ...)

## S3 method for class 'sobolEff'
autoplot(object, ...)

## S3 method for class 'sobolmartinez'
autoplot(object, ...)

## S3 method for class 'sobol_summary'
autoplot(object, ...)

Arguments

object

A sobol_result, sobol_summary, or sensitivity::sobol instance.

...

Further arguments passed to the plotting backend.

show_uncertainty

Logical, when TRUE bootstrap quantiles are computed (if available) and displayed as error bars.

probs

Numeric vector of probabilities used for the uncertainty bars.

bootstrap

Integer indicating how many bootstrap resamples to draw when show_uncertainty = TRUE.

separate_panels

Should the indices be plotted on separate panels according to their order? If separate_panels = TRUE, the first order indices are separated from the higher orders ones.

ncol

If separate_panels = TRUE, the number of columns for the facet wrapping of the plot.

Value

A ggplot object when ggplot2 is installed, otherwise the bar centres invisibly.

Bootstrap Sobol indices from stored samples

Description

Recompute Sobol first- and total-order indices from stored sample matrices using bootstrap resampling. Falls back to deterministic values when no samples are available.

Usage

bootstrap_indices(result, bootstrap)

Arguments

result

A sobol_result object produced by sobol_indices().

bootstrap

Integer indicating how many bootstrap replicates to draw.

Value

A list with matrices first and total containing the bootstrap replications.

Estimate Failure Probability from Simulator Outputs

Description

Convenient helper to compute the reliability-related probabilities described in Lebrun et al. (2021). The failure domain is controlled by a threshold and an inequality direction.

Usage

estimate_failure_probability(response, threshold, less = TRUE, weights = NULL)

Arguments

response

Numeric vector of simulator evaluations.

threshold

Numeric scalar defining the failure boundary.

less

Logical, failure is defined as response <= threshold when TRUE and response >= threshold otherwise.

weights

Optional numeric vector of non-negative weights. The vector is normalised internally when supplied.

Value

A list containing the estimated probability and its variance.

Examples

y <- rnorm(1000)
estimate_failure_probability(y, threshold = -1)

Fast Ishigami Test Function

Description

C++ implementation of the Ishigami function that is widely used as a benchmark for Sobol sensitivity indices. The implementation is vectorised and therefore convenient for Monte Carlo experiments.

Usage

ishigami_model(x, a = 7, b = 0.1)

Arguments

x

Numeric matrix with three columns representing the inputs.

a

Numeric scalar controlling the nonlinear term.

b

Numeric scalar controlling the interaction term.

Value

Numeric vector of simulator outputs.

Examples

x <- matrix(runif(30, -pi, pi), ncol = 3)
ishigami_model(x)

Simulate one unit in the simple process

Description

Internal helper. The output is a length-3 numeric vector: success indicator, waiting time to decision, and extra time if success.

Usage

one_unit(lambda1, lambda2, lambda3, p1, p2)

Arguments

lambda1, lambda2, lambda3

Positive rates.

p1, p2

Success probabilities.

Value

Numeric vector c(success, t_decision, extra_time_if_success).

Time to M successes for one individual

Description

Stochastic model that simulates successive units until M successes occur, and returns the time when the M-th success happens.

Usage

process_fun_indiv(X_indiv, M = 50)

Arguments

X_indiv

Numeric vector c(lambda1, lambda2, lambda3, p1, p2).

M

Target number of successes.

Value

Scalar time to M successes, with attribute "success".

QoI wrapper for the process model

Description

For each row of X, evaluates process_fun_row_wise several times and returns the mean time to M successes.

Usage

process_fun_mean_to_M(X, M = 50, nrep = 10)

Arguments

X

Matrix or data.frame of parameters.

M

Target number of successes.

nrep

Number of repetitions for the QoI.

Value

Numeric vector of QoI values.

Process model for a matrix of individuals

Description

Applies process_fun_indiv row-wise to a matrix of parameters.

Usage

process_fun_row_wise(X, M = 50)

Arguments

X

Matrix or data.frame with columns lambda1, lambda2, lambda3, p1, p2.

M

Target number of successes.

Value

Numeric vector of length nrow(X).

Two-step clinic model wrapper for Sobol designs

Description

Simulate a simple clinic with separate registration and examination stages using simmer. The quantity of interest is the mean time in system over nrep replications for each parameter set.

Usage

sobol4r_clinic_model(
  X,
  cap_reg = 2,
  cap_exam = 3,
  horizon = 2000,
  warmup_prob = 0.2,
  nrep = 10L
)

Arguments

X

Design matrix or data.frame with columns lambda (arrival rate), mu_reg (registration service rate), and mu_exam (examination service rate).

cap_reg, cap_exam

Integer capacities for the registration and examination resources.

horizon

Simulation horizon.

warmup_prob

Fraction of the horizon treated as warmup and discarded before computing the mean time in system.

nrep

Number of replications used to average the mean time in system.

Value

Numeric vector of length nrow(X).

Design generation for Sobol indices

Description

Simple helper that wraps sensitivity::sobol with model = NULL to create the extended design matrix used to evaluate the model.

Usage

sobol4r_design(
  X1,
  X2,
  order = 2,
  nboot = 0,
  type = c("soboljansen", "sobol", "sobol2007", "sobolEff", "sobolmartinez"),
  ...
)

Arguments

X1

First sample (matrix or data.frame).

X2

Second sample (matrix or data.frame).

order

Maximum interaction order (1 or 2).

nboot

Number of bootstrap replicates for confidence intervals.

type

Type of Monte Carlo Estimation of Sobol' Indices to be used. Supported estimators mirror the sensitivity helpers: sobol, sobol2007, soboljansen, sobolEff, and sobolmartinez. Defaults to "soboljansen", which is the safest general-purpose choice for both deterministic and stochastic simulators.

...

Additional arguments passed to sensitivity::sobol.

Value

An object of class "sobol" whose $X field contains the design matrix. You should evaluate your model on $X and then call sensitivity::tell().

M/M/1 queue model wrapper for Sobol designs

Description

Evaluate a simple M/M/1 queue built with simmer for each row of a Sobol design matrix. The quantity of interest is the mean time in system across nrep independent replications.

Usage

sobol4r_mm1_model(X, horizon = 1000, warmup = 200, nrep = 20L)

Arguments

X

Design matrix or data.frame with columns lambda (arrival rate) and mu (service rate).

horizon

Simulation horizon.

warmup

Warmup period; arrivals ending before this time are discarded from the summary statistic.

nrep

Number of replications used to average the mean time in system.

Value

Numeric vector of length nrow(X).

Generic QoI-based Sobol indices for a stochastic model

Description

This function extends the classical Sobol indices to a stochastic simulator by first computing a quantity of interest (QoI) for each input point, such as the mean of repeated runs.

Usage

sobol4r_qoi_indices(
  model,
  X1,
  X2,
  qoi_fun = base::mean,
  nrep = 1000,
  order = 2,
  nboot = 0,
  type = c("soboljansen", "sobol", "sobol2007", "sobolEff", "sobolmartinez"),
  ...
)

Arguments

model

Stochastic model function that takes a matrix or data.frame X and returns a numeric vector of length nrow(X).

X1, X2

Two base designs (matrices or data.frames).

qoi_fun

Function used to summarize the repetitions (default is mean).

nrep

Number of repetitions of the stochastic model for each design point.

order

Maximum interaction order (1 or 2).

nboot

Number of bootstrap replicates for Sobol indices.

type

Which estimator to use. Any sensitivity Sobol helper is supported: "sobol", "sobol2007", "soboljansen", "sobolEff", or "sobolmartinez". Defaults to "soboljansen", the most robust general-purpose choice.

...

Additional arguments passed to model.

Value

An object of class "sobol" with QoI-based Sobol indices.

Run Sobol analysis with optional QoI wrapper

Description

Helper around sensitivity::sobol that mimics the structure of the original scripts. It never writes to disk.

Usage

sobol4r_run(
  model,
  X1,
  X2,
  order = 2,
  nboot = 100L,
  qoi_fun = NULL,
  nrep = 1L,
  type = c("soboljansen", "sobol", "sobol2007", "sobolEff", "sobolmartinez"),
  ...
)

Arguments

model

Deterministic or stochastic model that takes a design X and returns a numeric vector of length nrow(X).

X1, X2

Matrices or data.frames used to build the Sobol design.

order

Order of the Sobol indices (1 or 2).

nboot

Number of bootstrap replicates for confidence intervals.

qoi_fun

Optional quantity of interest function. If not NULL, the model is evaluated repeatedly and QoI is computed row wise.

nrep

Number of replications per design row when qoi is not NULL.

type

Type of Monte Carlo Estimation of Sobol' Indices to be used. Supported estimators mirror the sensitivity helpers: sobol, sobol2007, soboljansen, sobolEff, and sobolmartinez. Defaults to "soboljansen" because it offers robust first and total order indices on both centred and non-centred outputs.

...

Extra arguments passed to model.

Value

A sobol object (output of sensitivity::tell).

Create Sobol Sampling Designs

Description

Generate the two-sample matrices (A and B) that are required to apply Monte Carlo Sobol estimators. The helper can rely on pseudo random numbers or on a light-weight Halton low-discrepancy sequence to increase coverage.

Usage

sobol_design(
  n,
  d,
  lower = rep(0, d),
  upper = rep(1, d),
  quasi = FALSE,
  seed = NULL
)

Arguments

n

Integer, number of rows per design matrix.

d

Integer, number of model parameters.

lower

Numeric vector of length d containing lower bounds.

upper

Numeric vector of length d containing upper bounds.

quasi

Logical, when TRUE a Halton sequence is used.

seed

Optional integer used to initialise the RNG state.

Value

A list with matrices A and B plus the column names.

Examples

design <- sobol_design(n = 64, d = 3, quasi = TRUE)
str(design)

Example 3: Large covariate dependent random effect

Description

Third input C3 is uniform on [1, 100], used as the mean of a Gaussian noise term added to the G-function. Quantity of interest is the mean of repeated evaluations.

Usage

sobol_example_covariate_large(
  n = 50000,
  nrep_qoi = 1000,
  order = 2,
  nboot = 100
)

Arguments

n

Monte Carlo sample size for each base design.

nrep_qoi

Number of repetitions for the QoI.

order

Maximum interaction order.

nboot

Number of bootstrap replicates.

Value

A list with two "sobol" objects: x_single (single noisy run), x_qoi (QoI-based indices).

Example 4: Slight covariate dependent random effect

Description

Same as sobol_example_covariate_large but with C3 uniform on [1, 1.5], that is with a much smaller range for the mean of the Gaussian noise.

Usage

sobol_example_covariate_small(
  n = 50000,
  nrep_qoi = 1000,
  order = 2,
  nboot = 100
)

Arguments

n

Monte Carlo sample size for each base design.

nrep_qoi

Number of repetitions for the QoI.

order

Maximum interaction order.

nboot

Number of bootstrap replicates.

Value

A list with two "sobol" objects: x_single (single noisy run), x_qoi (QoI-based indices).

Example 1: Deterministic G-function (reference case)

Description

Reproduces the classical non-random Sobol analysis on the G-function with k = 8 inputs on [0, 1].

Usage

sobol_example_g_deterministic(
  n = 50000,
  a = c(0, 1, 4.5, 9, 99, 99, 99, 99),
  order = 2,
  nboot = 100
)

Arguments

n

Monte Carlo sample size for each base design.

a

Parameter vector for the G-function.

order

Maximum interaction order for Sobol indices.

nboot

Number of bootstrap replicates.

Value

An object of class "sobol".

Example 5: Sobol indices for the process model

Description

Computes Sobol indices for the simple process example with random distributional parameters. Uses both a single trajectory and a QoI based on repeated runs.

Usage

sobol_example_process(n = 100, M = 50, nrep_qoi = 10, order = 1, nboot = 10)

Arguments

n

Monte Carlo sample size for each base design.

M

Target number of successes.

nrep_qoi

Number of repetitions for the QoI.

order

Maximum interaction order.

nboot

Number of bootstrap replicates.

Value

A list with two "sobol" objects: xp_single and xp_qoi.

Example 2: Random effect on the output (constant Gaussian noise)

Description

Two inputs in [0, 1], Sobol G-function with k = 2, plus additive Gaussian noise, and a QoI based on the mean of repeated evaluations.

Usage

sobol_example_random_output(
  n = 50000,
  sd = 1,
  nrep_qoi = 1000,
  order = 2,
  nboot = 100
)

Arguments

n

Monte Carlo sample size for each base design.

sd

Standard deviation of the Gaussian noise.

nrep_qoi

Number of repetitions for the QoI.

order

Maximum interaction order.

nboot

Number of bootstrap replicates.

Value

A list with three "sobol" objects: x_det (deterministic G-function), x_noise (single noisy output), x_qoi (QoI-based indices).

Sobol G-function restricted to the first two inputs

Description

Convenience wrapper around sobol_g_function that uses only the first two columns of X.

Usage

sobol_g2_R(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of model outputs.

Additive Gaussian noise on the Sobol G-function (k = 2) - C++ backend

Description

Additive Gaussian noise on the Sobol G-function (k = 2) - C++ backend

Usage

sobol_g2_additive_noise(X, sd = 1, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

sd

Standard deviation of the Gaussian noise.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of model outputs with noise.

Additive Gaussian noise on the Sobol G-function (k = 2)

Description

Additive Gaussian noise on the Sobol G-function (k = 2)

Usage

sobol_g2_additive_noise_R(X, sd = 1, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

sd

Standard deviation of the Gaussian noise.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of model outputs with noise.

Sobol G-function restricted to the first two inputs - C++ backend

Description

Convenience wrapper around sobol_g_function that uses only the first two columns of X.

Usage

sobol_g2_function(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of length nrow(X) with model outputs.

QoI wrapper for covariate noisy G-function (k = 2) - C++ backend

Description

Computes a mean over repeated evaluations of the noisy model.

Usage

sobol_g2_qoi_covariate_mean(
  X,
  nrep = 1000,
  a = c(0, 1, 4.5, 9, 99, 99, 99, 99)
)

Arguments

X

Numeric matrix or data.frame with at least two columns.

nrep

Number of replicates used for the QoI.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of QoI values (means over nrep runs).

Quantity-of-interest wrapper for the covariate noisy G-function (k = 2)

Description

Computes a mean over repeated evaluations of the noisy model.

Usage

sobol_g2_qoi_covariate_mean_R(
  X,
  nrep = 1000,
  a = c(0, 1, 4.5, 9, 99, 99, 99, 99)
)

Arguments

X

Numeric matrix or data.frame with at least two columns.

nrep

Number of replicates used for the QoI.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of QoI values (means over nrep runs).

QoI wrapper for the noisy G-function (k = 2) - C++ backend

Description

Computes a mean over repeated evaluations of the noisy model.

Usage

sobol_g2_qoi_mean(X, nrep = 1000, sd = 1, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

nrep

Number of replicates used for the QoI.

sd

Standard deviation of the Gaussian noise.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of QoI values (means over nrep runs).

Quantity-of-interest wrapper for the noisy G-function (k = 2)

Description

Computes a mean over repeated evaluations of the noisy model.

Usage

sobol_g2_qoi_mean_R(
  X,
  nrep = 1000,
  sd = 1,
  a = c(0, 1, 4.5, 9, 99, 99, 99, 99)
)

Arguments

X

Numeric matrix or data.frame with at least two columns.

nrep

Number of replicates used for the QoI.

sd

Standard deviation of the Gaussian noise.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of QoI values (means over nrep runs).

Covariate dependent Gaussian noise on the Sobol G-function (k = 2) - C++ backend

Description

Covariate dependent Gaussian noise on the Sobol G-function (k = 2) - C++ backend

Usage

sobol_g2_with_covariate_noise(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of model outputs with noise.

Additive Gaussian noise on the Sobol G-function (k = 2)

Description

Additive Gaussian noise on the Sobol G-function (k = 2)

Usage

sobol_g2_with_covariate_noise_R(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame with at least two columns.

a

Numeric vector of parameters (at least length 2).

Value

Numeric vector of model outputs with noise.

Sobol G-function (Saltelli reference function)

Description

Generic implementation of the Sobol G-function for k inputs. Columns of X are interpreted as inputs X1, X2, ..., Xk.

Usage

sobol_g_R(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame of inputs in [0, 1].

a

Numeric vector of parameters a_j controlling importance. Its length must be at least ncol(X).

Value

Numeric vector of length nrow(X) with model outputs.

Sobol G-function (Saltelli reference function) - C++ backend

Description

Generic implementation of the Sobol G-function for k inputs. Columns of X are interpreted as inputs X1, X2, ..., Xk.

Usage

sobol_g_function(X, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))

Arguments

X

Numeric matrix or data.frame of inputs in [0, 1].

a

Numeric vector of parameters a_j controlling importance. Its length must be at least ncol(X).

Value

Numeric vector of length nrow(X) with model outputs.

Sobol Indices for Stochastic Simulators

Description

Estimate first-order and total-order Sobol indices using Monte Carlo estimators that support noisy outputs via independent replicates.

Usage

sobol_indices(
  model,
  design,
  replicates = 1L,
  estimator = c("jansen", "saltelli"),
  keep_samples = FALSE,
  ...
)

Arguments

model

Function receiving a numeric matrix and returning a numeric vector of responses. The function may include internal randomness.

design

Output of sobol_design().

replicates

Integer, number of repeated evaluations to average out the model noise. Defaults to one replicate (deterministic behaviour).

estimator

Character string, either "saltelli" or "jansen". Defaults to "jansen".

keep_samples

When TRUE, store all simulated values.

...

Further arguments passed to model.

Details

Two families of estimators are available:

Value

An object of class sobol_result containing the indices, intermediate estimates, and the Monte Carlo variance.

Examples

design <- sobol_design(n = 128, d = 3, quasi = TRUE)
model <- function(x) ishigami_model(x)
result <- sobol_indices(model, design, replicates = 4)
result$data

Reliability-Oriented Sobol Indices

Description

Transform stored simulator samples into Sobol indices for the binary failure indicator described by Lebrun et al. (2021). The function reuses the Saltelli-type estimator from sobol_indices() and therefore requires a previous call with keep_samples = TRUE.

Usage

sobol_reliability(result, threshold, less = TRUE)

Arguments

result

Output of sobol_indices() computed with keep_samples = TRUE.

threshold

Numeric scalar defining the failure boundary.

less

Logical, when TRUE failures correspond to response <= threshold; otherwise, failures correspond to response >= threshold.

Value

A sobol_result instance storing the Sobol indices of the failure indicator along with the estimated failure probability and its variance.

Examples

design <- sobol_design(n = 128, d = 3, lower = rep(-pi, 3), upper = rep(pi, 3))
stochastic <- sobol_indices(ishigami_model, design, replicates = 3,
                            keep_samples = TRUE)
failure <- sobol_reliability(stochastic, threshold = -1)
Sobol4R::autoplot(failure, show_uncertainty = TRUE)

Summarise Sobol Indices

Description

Compute compact summaries of the Sobol indices and their Monte Carlo variability. The function is intended to feed diagnostic plots.

Usage

summarise_sobol(result, probs = c(0.1, 0.5, 0.9), bootstrap = 200L)

Arguments

result

A sobol_result object.

probs

Numeric vector of probabilities used to report quantiles of the empirical bootstrap distribution.

bootstrap

Integer, number of bootstrap resamples used to quantify the estimator uncertainty.

Value

A data frame (class sobol_summary) with the requested statistics. Quantile columns are added when probs is not empty.

Examples

design <- sobol_design(n = 64, d = 3)
model <- function(x) ishigami_model(x)
sob <- sobol_indices(model, design, keep_samples = TRUE)
summarise_sobol(sob, probs = c(0.1, 0.9))