Prediction

Prediction is a testable statement about an outcome, with a defined horizon and uncertainty. Improvement can come from better information, models, measurement, or aggregation, evaluated against appropriate outcomes and scoring rules.

A prediction states an outcome, time, and degree of uncertainty before the result is known. Evaluation needs a matching criterion: point estimates can be scored by error, while probability forecasts require assessment of calibration and informativeness. A clearly recorded forecast lets later results improve the process without rewriting what was originally expected.

For a numerical target and an arithmetic mean forecast, the mean's squared error equals average individual squared error minus the average squared spread around the mean. This is an algebraic identity, not an independence assumption. It shows the mean is no worse than the average member under that loss, but not necessarily better than the best member. Adding a poor forecaster can worsen the aggregate.

When to use it

When forecast quality needs systematic improvement; when the diversity prediction theorem would improve aggregate forecasting; when calibration between confidence and accuracy needs measurement; when distinguishing between predictable and unpredictable domains would improve strategy.

How it can help

Record forecasts before outcomes, use relevant baselines and scoring rules, and inspect errors across comparable cases. Combine forecasts when the resulting aggregate performs usefully, while accounting for shared mistakes and poor contributors.