Abstract
In this report a statistical t h eory of prediction that can be applied to the forecasting based on limited data or a small sample is outlined. The exact sampling prediction theory is framed on two foundation stones; the one is a two sample theory in which the multivariate regression theory is introduced, and the other is a theory of time series in which a sort of conditional independency is introduced for some types of processes that may be sufficiently general for practice.
From the fundamental theory some special prediction formulas are derived; for instance, the joint prediction of future changes, the prediction of the pattern of distribution of a meteorological element and so forth.
In order to express the uncertainty of a prediction an idea of stochastic prediction is introduced, which is defined by a sort of relative conditional probability distribution.
