Sensitivity Analysis Guidelines

Sensitivity Analysis Guidelines

Overview

Sensitivity analysis quantifies how input parameter variations affect simulation outputs. It helps identify the most influential parameters for calibration and uncertainty reduction.

Method Categories

Local Sensitivity (One-At-a-Time)

How It Works

Vary one parameter while holding others fixed at nominal values. Compute partial derivatives:

S_i = (dy/dx_i) * (x_i / y)  [normalized]

When to Use

• Quick screening
• Nearly linear response
• Local behavior near operating point

Limitations

• Misses parameter interactions
• Depends on chosen nominal point
• Invalid for nonlinear responses

Morris Method (Elementary Effects)

How It Works

Compute elementary effects by stepping through parameter space along random trajectories:

EE_i = [y(x + delta*e_i) - y(x)] / delta

Statistics computed:

• mu* (mean absolute EE): Overall importance
• sigma (std of EE): Nonlinearity/interactions

Interpretation

Sample Requirements

• Trajectories r: 10-50 (typically 20)
• Levels p: 4-8
• Total evaluations: r * (d + 1)

When to Use

• Moderate budgets
• Screening before detailed analysis
• Want to detect interactions

Sobol Indices (Variance-Based)

How It Works

Decompose output variance into contributions from each parameter and their interactions:

V(Y) = sum(V_i) + sum(V_ij) + ... + V_12...d

Indices:

• S_i (first-order): Main effect of parameter i
• S_Ti (total): Main + all interactions involving i

Interpretation

Sample Requirements

For Saltelli estimator:

• Base samples N: 512, 1024, 2048
• Total evaluations: N * (d + 2)

When to Use

• Quantitative variance attribution needed
• Sufficient budget for global analysis
• Nonlinear, interacting models

Interpreting Rankings

Score Thresholds

When Rankings Are Close

If top parameters have similar scores:

1. Check for interactions (S_Ti >> S_i)
2. Consider fixing less important parameters
3. Use higher sample sizes for better precision

Red Flags

Visualization Recommendations

Bar Charts

Plot parameters sorted by sensitivity score with confidence intervals.

kappa       ████████████████████ 0.52
mobility    ███████████ 0.28
W           ██████ 0.15
rho         ██ 0.05

Interaction Heatmaps

For second-order indices S_ij, use heatmap with parameters on both axes.

Scatter Plots

Plot output vs each input to visually confirm sensitivity rankings.

Common Pitfalls

Implementation Notes

The sensitivity_summary.py script in this skill:

• Takes pre-computed sensitivity scores as input
• Ranks parameters from most to least influential
• Flags if all sensitivities are very low
• Returns structured JSON for downstream use

For computing Sobol indices, use external tools:

• SALib (Python, comprehensive)
• sensitivity (R package)
• UQlab (MATLAB)