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title

Sensitivity Analysis

매 한 줄

"매 input 변동이 output 의 어디에 얼마나 영향?". 매 Sobol indices (variance decomposition), Morris elementary effects (screening), 그리고 ML interpretability (SHAP, permutation importance) 모두 매 sensitivity analysis 의 family. 매 2026 default: SALib (classic SA) + SHAP (ML model).

매 핵심

매 Local vs Global

Local: gradient at one point (∂y/∂x). 매 빠르지만 nonlinear 모델 misleading.
Global: full input space sample. 매 Sobol/Morris/FAST. 매 정직.

매 Method 분류

Screening (Morris): 매 cheap, identify important factors among many. r·(k+1) runs.
Variance-based (Sobol): S1 (first-order), ST (total). 매 N·(2k+2) Saltelli sample.
Regression-based: standardized regression coefficients (SRC).
ML feature importance: permutation, SHAP, integrated gradients.

매 응용

Engineering tolerance — 매 어느 parameter 가 yield drop.
Climate/epidemiology model — input uncertainty propagation.
ML model debug — 매 feature 가 prediction drive.
Hyperparameter search prior — 매 important hp 만 tune.

💻 패턴

Sobol indices (SALib)

from SALib.sample import saltelli
from SALib.analyze import sobol
import numpy as np

problem = {
    'num_vars': 3,
    'names': ['x1', 'x2', 'x3'],
    'bounds': [[0, 1]] * 3,
}
param_values = saltelli.sample(problem, 1024)
Y = np.array([model(*row) for row in param_values])
Si = sobol.analyze(problem, Y)
print(Si['S1'], Si['ST'])  # first-order + total

Morris screening

from SALib.sample.morris import sample
from SALib.analyze import morris

X = sample(problem, N=100, num_levels=4)
Y = np.array([model(*r) for r in X])
Mi = morris.analyze(problem, X, Y, num_levels=4)
print(Mi['mu_star'], Mi['sigma'])  # importance, nonlinearity

Permutation importance (sklearn)

from sklearn.inspection import permutation_importance
r = permutation_importance(model, X_val, y_val, n_repeats=20, random_state=0)
for i in r.importances_mean.argsort()[::-1]:
    print(f"{features[i]}: {r.importances_mean[i]:.3f} ± {r.importances_std[i]:.3f}")

SHAP for any model

import shap
explainer = shap.TreeExplainer(xgb_model)  # or shap.Explainer for general
sv = explainer(X_val)
shap.plots.beeswarm(sv)         # global
shap.plots.waterfall(sv[0])     # local

Tornado plot (one-at-a-time)

base = model(**defaults)
deltas = []
for k, (lo, hi) in bounds.items():
    lo_y = model(**{**defaults, k: lo})
    hi_y = model(**{**defaults, k: hi})
    deltas.append((k, hi_y - lo_y))
deltas.sort(key=lambda x: abs(x[1]), reverse=True)

Variance decomposition w/ ANOVA

import statsmodels.api as sm
from statsmodels.formula.api import ols
m = ols('y ~ x1 + x2 + x3 + x1:x2', data=df).fit()
print(sm.stats.anova_lm(m, typ=2))

매 결정 기준

상황	Approach
100+ inputs, screen first	Morris
<20 inputs, full ranking	Sobol
ML black-box	SHAP / permutation
Linear-ish model	SRC
One-shot intuition	Tornado

기본값: SALib Sobol (simulation), SHAP (ML model).

🔗 Graph

부모: Statistics · Epistemic-Uncertainty
변형: SHAP
응용: Hyperparameters
Adjacent: Bayesian Inference · Monte-Carlo

🤖 LLM 활용

언제: simulation/model에서 어느 input이 결과 좌우하는지 정량화. ML feature 중요도 ranking. 언제 X: input 간 강한 correlation 존재 — Sobol 가정 깨짐. Conditional SA / Shapley 사용.

❌ 안티패턴

OAT only: one-at-a-time 은 interaction 놓침.
Sample 너무 작음: Sobol N<512 → 매우 noisy estimate.
Correlated inputs 무시: independence 가정 violation.
SHAP = causal: SHAP 는 attribution, causality 아님.

🧪 검증 / 중복

Verified (Saltelli 2010, SALib docs, scikit-learn inspection).
신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — Sobol/Morris/SHAP unified treatment

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