Non-Uniform Inputs

Use this page when your Sobol analysis needs independent inputs with different marginals. gsax.Problem.from_dict(...) accepts the legacy (low, high) uniform shorthand plus tagged TypedDict specs for Gaussian and truncated Gaussian inputs.

Define a mixed-input problem

python

import jax.numpy as jnp
import numpy as np
from scipy.stats import truncnorm

import gsax

problem = gsax.Problem.from_dict(
    {
        "uniform": (0.0, 2.0),
        "gaussian": {
            "dist": "gaussian",
            "mean": 1.0,
            "variance": 2.25,
        },
        "truncated": {
            "dist": "gaussian",
            "mean": 0.5,
            "variance": 1.44,
            "low": -0.5,
            "high": 1.0,
        },
    },
    output_names=("response",),
)

Rules for Gaussian specs:

mean and variance describe the parent Gaussian before truncation.
low and high are optional and may be used independently.
When either truncation bound is present, gsax.sample() uses a true truncated normal transform, not hard clipping.

Run Sobol on a single-timepoint linear model

For a linear model

y = \sum_{i} a_{i} x_{i}

the analytical first-order and total-order Sobol indices are identical:

S_{i} = \frac{a_{i}^{2} Var (X_{i})}{\sum_{j} a_{j}^{2} Var (X_{j})}

The snippet below keeps the output layout as (N, 1, 1) so you can compare one timepoint/output slice directly.

python

coeffs = jnp.array([1.5, -0.75, 2.0])

sampling_result = gsax.sample(
    problem,
    n_samples=8192,
    calc_second_order=False,
    seed=101,
)

X = jnp.asarray(sampling_result.samples)
Y = (X @ coeffs)[:, None, None]  # (N, 1, 1)

result = gsax.analyze(sampling_result, Y)

std = np.sqrt(1.44)
a = (-0.5 - 0.5) / std
b = (1.0 - 0.5) / std

variances = np.array(
    [
        (2.0 - 0.0) ** 2 / 12.0,
        2.25,
        truncnorm.var(a, b, loc=0.5, scale=std),
    ]
)
weights = np.square(np.asarray(coeffs)) * variances
analytical = weights / weights.sum()

print("Computed S1:", np.asarray(result.S1[0, 0]))
print("Computed ST:", np.asarray(result.ST[0, 0]))
print("Analytical:", analytical)

Expected behavior:

result.S1[0, 0, :] and result.ST[0, 0, :] should closely match the analytical variance ratios.
result.S2 is None because calc_second_order=False.

Practical notes

problem.bounds is None as soon as any Gaussian spec is present. This is expected and signals that the problem is not finite-bounds-only anymore.
Save/load still works for mixed problems. The JSON metadata records the declared input specs so gsax.load() can reconstruct the same marginals.
analyze_hdmr() supports non-uniform inputs (Gaussian, truncated Gaussian) via CDF mapping to [0, 1] before surrogate fitting.

Non-Uniform Inputs ​

Define a mixed-input problem ​

Run Sobol on a single-timepoint linear model ​

Practical notes ​

See also ​

Non-Uniform Inputs

Define a mixed-input problem

Run Sobol on a single-timepoint linear model

Practical notes

See also