📉 Prediction Intervals (PI)

Prediction Intervals (PI)#

A range expected to contain the outcome with a stated probability.

Important

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What it is#

A prediction interval is a range \([\,\text{lower},\ \text{upper}\,]\) expected to contain the future observation with a stated probability — its nominal coverage, e.g. 90%. It is typically built from a pair of quantiles, the \((1-\alpha)/2\) and \((1+\alpha)/2\) levels (the 5th and 95th percentiles for 90% coverage):

\[\big[\, \hat{Q}_{(1-\alpha)/2},\ \ \hat{Q}_{(1+\alpha)/2} \,\big] \quad\Rightarrow\quad \text{nominal coverage } 1-\alpha.\]

Coverage vs width#

Quality trades coverage — does the empirical fraction of actuals landing inside match the nominal level? — against width / sharpness — narrower is more useful, but only if coverage holds. (A PI is about a future value, distinct from a confidence interval, which is about a parameter.)

Calibrating them#

Conformal prediction is a model-agnostic wrapper that adjusts interval width on a held-out calibration set to guarantee the target coverage in finite samples, under mild assumptions.

Theme: Risk & Probabilistic Forecasting · All terminology

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Mind map — connected ideas

Quantile Forecasts · Quantile Regression · Probabilistic Forecasts · Continuous Probabilistic Forecasts · Quantile Level · Strictly Proper Scoring Rules

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