Application of statistical estimators to analysis and prediction is examined from the point of view of geophysical fluid dynamics. The fundamental difficulty is that estimators constructed from observational records of limited length (the usual case in GFD) are sensitive to sampling errors in the statistics upon which they are based. To achieve meaningful results, the number of data, or input, parameters must be limited. The relationship between statistical and dynamical models (particularly clear for linear systems) coupled with certain statistical methods are explored with respect to the problem of input parameter selection, both for linear and nonlinear systems. Methods of assessing the effects of sampling errors in hindcasts are discussed and techniques for minimizing these effects in forecasts are evaluated. A method of efficiently condensing statistical models to a few input parameters and transfer functions is given. Finally the steps of hindcast analysis and forecaster construction are discussed from the practical point of view.