# Prequential Principle

There are several varieties of the prequential principle: weak, strong, and superstrong. By default, "prequential principle" means "weak prequential principle", and this is what is described in this article.

We are interested in criteria of agreement between the forecasts output by Forecaster and the actual outcomes chosen by Nature. All prequential principles are requirements for such criteria. In some cases, Forecaster and Nature may follow deterministic or stochastic strategies in choosing their moves. In other cases, their moves may be regarded as simply produced when required, with no underlying strategy. The *weak prequential principle* requires that any criterion of agreement should depend only on the actual observed sequences of forecasts and outcomes, and not further on the strategies (if any) which might have produced these.

The likelihood principle appears to have been the original motivation behind the prequential principle (Dawid, 1984).

### Bibliography

- A. P. Dawid. Present position and potential developments: some personal views. Statistical theory. The prequential approach (with discussion).
*Journal of the Royal Statistical Society A*147:278 - 292, 1984. The weak prequential principle is first stated (Section 5.1). - A. P. Dawid. Calibration-based empirical probability (with discussion).
*Annals of Statistics*13:1251 - 1285, 1985. The weak prequential principle is stated as metacriterion M2. - A. P. Dawid. Fisherian inference in likelihood and prequential frames of reference (with discussion).
*Journal of the Royal Statistical Society B*53:79 - 109, 1991. Section 7.2 is devoted to the weak prequential principle. - A. P. Dawid. Prequential analysis. In:
*Encyclopedia of Statistical Sciences*, update volume 1, S. Kotz, Editor-in-Chief, pp. 464 - 470. Wiley, 1997. The strong prequential principle is first stated. - A. P. Dawid and V. G. Vovk. Prequential probability: Principles and properties.
*Bernoulli*5:125 - 162, 1999. The strong and superstrong prequential principles are discussed.