Choosing a method

jaxgsa provides thirteen global sensitivity analysis methods. Choose one by the question you want to answer, the data you have, and the model evaluations you can afford.

If this is your first analysis, start with Sobol when you can run the model at new points. Start with a given-data method when the model runs already exist. For definitions of the reported quantities, read GSA concepts.

Decide in three questions

1. Can you run the model at new points?

Four methods build a dedicated design: Sobol, eFAST, Morris, and Kucherenko. They require model evaluations at the points returned by sample().

The other nine methods use ordinary input samples. Pass the input matrix X and model output Y to analyze(). DGSM also takes the model itself so it can compute derivatives, but it does not require a dedicated design.

2. What should the result mean?

Goal	Use	Result
Attribute output variance	Sobol, eFAST, PCE, HDMR	First-, total-, or higher-order variance contributions
Allocate variance to one number per parameter	Shapley	Shares that sum to one
Screen many parameters cheaply	Morris, DGSM	Elementary effects or derivative-based bounds
Measure changes to the full output distribution	PAWN, Borgonovo, optimal transport	CDF, density, or transport distances
Test general dependence	HSIC	Dependence indices and permutation p-values
Separate effects under dependent inputs	Kucherenko, VKOGA, HDMR	Conditional-variance or ANCOVA quantities

These results are not interchangeable. A Morris score is not a variance fraction, and a distributional distance need not rank parameters like a Sobol index. Choose the quantity before comparing the numbers.

3. What is the evaluation budget?

Sobol uses $N (D + 2)$ model runs for first- and total-order indices, or $N (2 D + 2)$ when second-order indices are requested.
Morris uses $r (D + 1)$ runs, where $r$ is the number of trajectories.
Kucherenko uses $N (2 D + 1)$ runs.
eFAST uses one search curve per parameter; its minimum design grows quadratically with the number of parameters.
Given-data methods require no new model evaluations, although their analysis time and memory requirements differ.
DGSM evaluates model Jacobians. Its cost depends on the input and output dimensions and the automatic-differentiation direction.

Here $D$ is the number of parameters and $N$ is a method-specific base sample count. For high-dimensional planning, see Scaling to large problems.

Common choices

Start with Sobol

Use Sobol when the inputs are independent, you can choose the evaluation points, and you want first-order, total-order, or pairwise interaction indices. It is the most direct general-purpose variance decomposition in the package.

python

import jaxgsa
from jaxgsa.benchmarks.ishigami import PROBLEM, evaluate

samples = jaxgsa.sobol.sample(PROBLEM, 8192, seed=0)
Y = evaluate(samples.samples)
result = jaxgsa.sobol.analyze(samples, Y)

print(result.S1)
print(result.ST)

Read the Sobol API for estimator choices, confidence intervals, and second-order indices. See the basic example for a full workflow.

Screen before a costly analysis

Use Morris when model evaluations dominate the budget. Use DGSM when the model is written in JAX and its derivatives are meaningful. Both methods are most useful for identifying parameters that have little influence; neither reports the same quantity as a Sobol index.

After screening, fix negligible parameters and run a variance-based analysis on the remaining set. The screen-first workflow shows this sequence.

When you already have data

Choose by the result you need:

PCE returns variance indices and a reusable polynomial surrogate.
HDMR returns component-wise variance contributions and a reusable spline surrogate.
Shapley returns one variance allocation per parameter.
VKOGA returns dependent-input variance quantities through a kernel surrogate.
PAWN, Borgonovo, and optimal transport compare output distributions rather than variance alone.
HSIC measures dependence and supplies permutation p-values.
DGSM evaluates derivatives of a JAX model at ordinary sample points.

Surrogate-based indices are only as reliable as the fitted surrogate. Check the fit diagnostics before interpreting PCE, HDMR, VKOGA, or Shapley results.

When inputs are dependent

There is no single extension of Sobol indices to dependent inputs. Kucherenko, VKOGA, HDMR, and the HDMR-backed Shapley route answer different questions. Distribution-based methods accept dependence but include both direct and correlation-borne influence in their scores.

Use Sensitivity with dependent inputs to choose among these definitions. Do not compare their values directly with classical Sobol indices for independent inputs.

When inputs are categorical

Sobol, PAWN, Borgonovo, and optimal transport accept unordered categorical parameters. The other methods refuse them because their results would depend on the arbitrary numeric coding of the levels.

See Categorical inputs for a worked comparison.

When you need gradients through the analysis

Most methods expose a pure indices() computation that can participate in JAX transformations. This is different from DGSM, which differentiates the model to define its sensitivity measure.

Support varies by method and transformation. Read Differentiating sensitivity analyses before building an end-to-end differentiable workflow.

Compare the methods

Direct variance methods

Method	Choose it when	Main trade-off
Sobol	You want $S_{1}$ , $S_{T}$ , and optional $S_{2}$ for independent inputs	Requires a Saltelli design
eFAST	You want $S_{1}$ and $S_{T}$ from Fourier search curves	Design size grows quickly with $D$
Kucherenko	You can run a dedicated design under declared input dependence	Indices have dependence-specific interpretations

Surrogate variance and allocation methods

Method	Choose it when	Main trade-off
PCE	A polynomial surrogate fits the response and you want $S_{1}$ , $S_{T}$ , or $S_{2}$	Expansion size grows with dimension and order
HDMR	You want component functions and an ANCOVA decomposition	Fit cost grows with interaction order
VKOGA	Inputs are dependent and you want several conditional-variance quantities	Results depend on a kernel surrogate
Shapley	You want one allocation per parameter that sums to one	Allocation depends on the PCE or HDMR fit

Screening and bounds

Method	Choose it when	Main trade-off
Morris	You need a low-cost first pass over many parameters	Reports screening statistics, not variance fractions
DGSM	The JAX model is differentiable and derivative-based bounds are useful	Bounds may be loose; long outputs increase Jacobian cost

Distribution and dependence measures

Method	Choose it when	Main trade-off
HSIC	You want a general dependence measure and permutation test	Kernel and permutation cost grow with sample size
PAWN	You want a CDF-based measure	Conditional binning introduces a tuning choice
Borgonovo	You want a density-based measure of distributional change	Conditional density estimation needs enough data
Optimal transport	You want mean-shift and shape-change contributions or a joint trajectory score	Transport solves cost more than simple univariate statistics

Method capabilities

This is the canonical compatibility table. “Own design” means the method provides sample() and must evaluate the model on that design. A cross means the method refuses the declared input type rather than silently approximating it.

Method	Reports	Own design	Correlated	Categorical	Bootstrap CI
`borgonovo`	$δ$ , $S_{1}$	✗	✓ §	✓	`n_bootstrap`
`dgsm`	bounds on $S_{T}$	✗	✗	✗	`n_bootstrap`
`efast`	$S_{1}$ , $S_{T}$	✓	✗	✗	—
`hdmr`	$S_{a}$ / $S_{b}$ / $S$ per term, surrogate	✗	✓ †	✗	`n_bootstrap`
`hsic`	dependence measure	✗	✓ §	✗	—
`kucherenko`	$S_{1}$ , $S_{T}$ under dependence	✓	✓	✗	`n_bootstrap`
`morris`	$μ^{*}$ , $σ$	✓	✗	✗	`n_bootstrap`
`optimal_transport`	$W_{2}^{2}$ index, advective + diffusive	✗	✓ §	✓	`n_bootstrap`
`pawn`	KS distance	✗	✓ §	✓	`n_bootstrap`
`pce`	$S_{1}$ , $S_{2}$ , $S_{T}$ , surrogate	✗	✗	✗	`n_bootstrap`
`shapley`	allocation summing to 1	✗	✗ ‡	✗	`n_bootstrap`
`sobol`	$S_{1}$ , $S_{2}$ , $S_{T}$	✓	✗	✓	`n_bootstrap`
`vkoga`	$S_{T C}$ , $S_{T U}$ , $S_{U}$ , $S_{C}$ , $S_{I U}$ , surrogate	✗	✓	✗	`n_bootstrap`

† HDMR accepts dependent inputs through its ANCOVA decomposition. Its $S_{T}$ is not a classical total-effect index under dependence.

‡ The default PCE-backed Shapley analysis refuses dependent inputs. The HDMR backend accepts them, and include_correlative=True includes the ANCOVA correlative contribution in the allocation.

§ These measures include correlation-borne influence. A parameter may score above zero because it is correlated with a parameter used by the model.

All methods support scalar, multi-output, and time-series outputs. Eleven methods offer bootstrap confidence intervals through n_bootstrap; eFAST has no row-bootstrap interval, while HSIC reports permutation p-values. The API overview documents the shared result shape.

Most methods also accept irregular output grids: pass each channel as a (times, values) pair when channels do not share the same time coordinates. The analyzer buckets compatible channels without padding and preserves their coordinates in the returned result. See Irregular output grids for the supported-method matrix and limitations.

Where to go next

Read GSA concepts to understand the reported quantities.
Read Sensitivity with dependent inputs when the parameters are correlated.
Read Scaling to large problems before committing a large evaluation budget.
Open a method's API reference for its complete signature and estimator details.
Browse the examples for complete analyses and output.

Choosing a method ​

Decide in three questions ​

1. Can you run the model at new points? ​

2. What should the result mean? ​

3. What is the evaluation budget? ​

Common choices ​

Start with Sobol ​

Screen before a costly analysis ​

When you already have data ​

When inputs are dependent ​

When inputs are categorical ​

When you need gradients through the analysis ​

Compare the methods ​

Direct variance methods ​

Surrogate variance and allocation methods ​

Screening and bounds ​

Distribution and dependence measures ​

Method capabilities ​

Where to go next ​