Post-fit analysis

Quantify a fit’s uncertainty with iws.LinearConfidenceInterval and iws.SobolSensitivity as pipeline elements.

A fit gives you parameter values. Post-fit analysis tells you how much to trust them: how tightly the data constrains each parameter, and which parameters the model output actually responds to.

Both run as pipeline elements, alongside the fit rather than after it in your own code, so the expensive part happens on the platform. For the concepts behind variance-based sensitivity, see the Sensitivity Analysis Guide.

The two elements

Schema	Answers
iws.LinearConfidenceInterval	How tightly does the data constrain each fitted parameter?
iws.SobolSensitivity	Which parameters does the model output respond to, and which interact?

Both take the same objectives and parameters as a DataFit. They accept only a PointEstimate optimizer, because they analyse a fit rather than performing one.

Adding analysis to a pipeline

Place the analysis element after the fit it analyses. When its objectives and parameters match the fit’s, it picks up the fitted point automatically — you do not restate the values:

import ionworks_schema as iws

pipeline = iws.Pipeline(
    {
        "fit": iws.DataFit(objectives=objectives, parameters=parameters),
        "intervals": iws.LinearConfidenceInterval(
            objectives=objectives,
            parameters=parameters,
        ),
        "sensitivity": iws.SobolSensitivity(
            objectives=objectives,
            parameters=parameters,
        ),
    }
)

Options

Both elements work with their defaults; these adjust what they compute.

iws.LinearConfidenceInterval

Option	Default	Description
confidence_level	0.95	Central probability mass for each interval. Use 0.99 for wider intervals, 0.68 for one-sigma.
use_parameter_bounds	True	Clip intervals to the parameter bounds, so an interval never extends into values the fit could not have returned.
variable_standard_deviations	None	Per-variable measurement noise standard deviations, as a mapping. Supply these when you know your instrument’s noise; otherwise it is estimated from the fit residuals.
gauss_newton	True	Use the Gauss-Newton Hessian approximation.

intervals = iws.LinearConfidenceInterval(
    objectives=objectives,
    parameters=parameters,
    confidence_level=0.99,
)

iws.SobolSensitivity

Option	Default	Description
n_samples	256	Base sample count for the Sobol design. This is the cost knob — see the note below.
calc_second_order	False	Also compute second-order indices, which report how parameters interact in pairs rather than only their individual effect. Raises the evaluation count.
use_log_transform	False	Sample parameters in log space. Appropriate when a parameter ranges over orders of magnitude.

sensitivity = iws.SobolSensitivity(
    objectives=objectives,
    parameters=parameters,
    n_samples=512,
    calc_second_order=True,
)

Reading the results

Each element returns a typed result, reachable off the pipeline result rather than by reading raw job metadata:

result = client.pipeline.result(pipeline_id)

intervals = result.element("intervals")     # iws.ConfidenceIntervalResult
sensitivity = result.element("sensitivity") # iws.SensitivityResult

Sobol sensitivity is a sampling method, so its cost grows with the number of parameters and with n_samples — the design uses n_samples x (n_params + 2) evaluations, rising to n_samples x (2 x n_params + 2) when calc_second_order=True. Start with a small parameter set and the default n_samples, and widen either once you know which parameters matter.