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An interval that, with a specified probability, contains a single future observation given the model and observed data.
DESCRIPTION
Prediction intervals quantify uncertainty around future observations rather than parameter estimates. They combine model uncertainty and residual variability. In linear models, intervals depend on error variance and leverage. For forecasting, they widen over horizon and incorporate noise and drift. Bayesian approaches use posterior predictive distributions. Proper coverage requires assumptions like residual independence and homoscedasticity or robust alternatives.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistical inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed.
Emphasizes future observations and conditional nature.
NIST Engineering Statistics Handbook
Prediction intervals provide a range of values that is likely to contain the value of a future observation from a process, given current information.
Focuses on process context and practical interpretation.
RELATED TERMS
Forecast Interval Uncertainty Quantification Bayesian Predictive Bootstrap Homoscedasticity Residuals Time Series Forecasting Credible Interval Prediction Error
COMPETING TERMS
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist BI Specialist Data Analyst AI Engineer
EXTERNAL SOURCES
- Wikipedia - Prediction interval
- NIST - Prediction intervals overview
- Forecasting: Principles and Practice - Forecasting intervals tutorial
TOP QUESTIONS
What distinguishes a Prediction Interval from a Confidence Interval?
Prediction intervals target future observations; confidence intervals target unknown parameters’ plausible values.
Category: Misunderstanding
How do model assumptions affect Prediction Intervals?
Violations like heteroscedasticity or autocorrelation can lead to miscalibrated coverage.
Category: Risks
How do Prediction Intervals change across forecast horizons?
They typically widen with horizon due to accumulating uncertainty.
Category: Overview
What are common mistakes with Prediction Intervals?
Confusing them with parameter uncertainty and ignoring residual diagnostics.
Category: Mistakes
How are Bayesian Prediction Intervals computed?
From the posterior predictive distribution by integrating parameter uncertainty and noise.
Category: Definition
How do you validate Prediction Interval coverage?
Use backtesting with coverage metrics and calibration plots across time.
Category: Requirements
What impacts interval width in regression?
Error variance, sample size, leverage, and model fit affect width.
Category: Overview
How do you communicate Prediction Intervals to stakeholders?
Present central forecasts with shaded interval bands and explain probability coverage.
Category: Best practices
Are Prediction Intervals useful for classification?
They’re primarily for numeric predictions; classification uses calibrated probabilities and thresholds.
Category: Misunderstanding