environmentaltools.temporal.confidence_intervals

environmentaltools.temporal.confidence_intervals(boot, alpha, resample, *args)[source]

Calculate confidence intervals using percentile or BCa bootstrap methods.

Computes confidence intervals for bootstrap resampling results using either standard percentile method or bias-corrected and accelerated (BCa) method.

Parameters:

  • boot (np.ndarray) – Bootstrap resampling matrix with shape (n_simulations, n_parameters)

  • alpha (float) – Significance level (e.g., 0.05 for 95% confidence intervals)

  • resample ({'standard', 'bca'}) –

    Method for estimating confidence intervals:

    • ’standard’: Simple percentile method

    • ’bca’: Bias-corrected and accelerated bootstrap

  • *args (tuple, optional) –

    Additional arguments required for BCa method: (orig, nosim, peaks, tri, tipo, nyears) where:

    • origarray-like

      Original parameter estimates

    • nosimint

      Number of bootstrap simulations

    • peaksarray-like

      Original peak time series

    • triarray-like

      Return periods

    • tipostr or scipy.stats distribution

      Distribution type

    • nyearsint

      Number of years in the dataset

Returns:

Confidence interval bounds with shape (2, n_parameters):

  • ci[0, :] : lower bounds

  • ci[1, :] : upper bounds

Return type:

np.ndarray

Notes

The BCa method adjusts for bias and skewness in the bootstrap distribution using acceleration (a) and bias-correction (z0) factors. It provides more accurate intervals than standard percentiles, especially for small samples or skewed distributions.

The acceleration factor is computed using jackknife influence values: a = sum(U^3) / [6 * sum(U^2)^(3/2)]

where U are the jackknife deviations.

References

Efron, B. (1987). “Better Bootstrap Confidence Intervals”. Journal of the American Statistical Association, 82(397), 171-185.

Examples

>>> boot = np.random.randn(1000, 3)  # Bootstrap samples
>>> ci = confidence_intervals(boot, alpha=0.05, resample='standard')
>>> print(f"95% CI: [{ci[0, 0]:.3f}, {ci[1, 0]:.3f}]")