environmentaltools.temporal.confidence_bands

environmentaltools.temporal.confidence_bands(rmse, n, confidence_level)[source]

Calculate confidence bands for model predictions using RMSE.

Computes confidence intervals around model predictions based on Root Mean Square Error and sample size using Student’s t-distribution.

Parameters:

  • rmse (float) – Root Mean Square Error of the model predictions

  • n (int) – Number of data points used in the model

  • confidence_level (float) – Confidence level for the interval (e.g., 0.95 for 95% confidence)

Returns:

Half-width of the confidence band (margin of error)

Return type:

float

Notes

The confidence band is calculated as:

margin = t_critical * (rmse / sqrt(n))

where t_critical is the critical value from Student’s t-distribution for the specified confidence level and n-1 degrees of freedom.

The prediction interval is then: [prediction - margin, prediction + margin]

Examples

>>> margin = confidence_bands(rmse=0.5, n=100, confidence_level=0.95)
>>> # Prediction interval: [y_pred - margin, y_pred + margin]