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Uncertainty Quantification (Monte Carlo & LHS)

fastspa supports uncertainty propagation by repeatedly sampling uncertain inputs and re-running SPA.

Monte Carlo uncertainty​

from fastspa import SPA

spa = SPA(A, emissions, sectors=sectors)

mc = spa.monte_carlo(
    sector=42,
    depth=8,
    n_samples=500,
    intensity_cv=0.2,      # 20% coefficient of variation on direct intensities
    distribution="lognormal",
    seed=42,
)

print(mc.total_intensity.mean, mc.total_intensity.ci_low, mc.total_intensity.ci_high)

Sector contribution uncertainty​

Monte Carlo results report uncertainty on leaf-sector contributions.

sector_stats = mc.sector_contributions
print(sector_stats[10].mean, sector_stats[10].ci_low, sector_stats[10].ci_high)

If pandas is installed:

mc.sector_contributions_dataframe()

Latin Hypercube Sampling (LHS)​

For the same distributional assumptions, LHS can reduce variance in estimates with fewer samples.

mc_lhs = spa.monte_carlo(
    sector=42,
    depth=8,
    n_samples=200,
    intensity_cv=0.2,
    sampling="lhs",
    seed=42,
)

Sensitivity (elasticities)​

Compute elasticities of total intensity to each direct intensity:

sens = spa.sensitivity(sector=42)

These elasticities sum to 1.0 for a given target sector.