Description
Add width, 2/alpha times any shortfall below lower, and 2/alpha times any exceedance above upper.
An interval forecast has both a width and a relationship to an observed value. Scoring rules can penalize narrow misses while boundary conventions determine coverage separately.
Add width, 2/alpha times any shortfall below lower, and 2/alpha times any exceedance above upper.
When to use this tool
Use Metrics: Interval Score Observation when you need one interval width, coverage, penalty, or error-envelope term.
How to use the tool and how it works
- Enter actual, lower, upper, alpha. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require ordered bounds and alpha in (0, 1). Add width, 2/alpha times any shortfall below lower, and 2/alpha times any exceedance above upper.1
For a central prediction interval, alpha is the total nominal probability outside the interval, with alpha/2 in each tail. The interval score combines width with a penalty for observations outside the bounds; lower scores are preferred.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| actual | Observed value on the same scale and unit as its prediction. | Required. Finite number. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| alpha | Nominal interval miscoverage as a fraction, not a percentage. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.width | Width | Calculated result member: number. |
| result.lowerPenalty | Lower Penalty | Calculated result member: number. |
| result.upperPenalty | Upper Penalty | Calculated result member: number. |
| result.score | Score under the explicit mathematical and availability conventions above. | Calculated result member: number. |
{
"input": {
"actual": 0,
"lower": 1,
"upper": 3,
"alpha": 0.2
},
"output": {
"result": {
"width": 2,
"lowerPenalty": 10,
"upperPenalty": 0,
"score": 12
}
}
}Limitations and assumptions
- Alpha is fractional miscoverage; this is a single-observation score with separately reported penalties, not empirical coverage.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Aggregate scores over comparable observations and examine empirical coverage and interval width together.
References
-
Calculation and input contract: metrics/interval-score-observation — tool.io
-
Strictly Proper Scoring Rules, Prediction, and Estimation — Tilmann Gneiting and Adrian E. Raftery / Journal of the American Statistical Association
Similar or alternative tools
- Winkler Score Width Penalty Split
Return interval width plus a penalty of 2/alpha times the distance below lower or above upper; observations within the interval add no penalty.
- Interval Score Missing Endpoint Case
With both endpoints present, validate their order and calculate width plus scaled outside penalties; otherwise return score zero, defined false, and missing endpoint names.