An Illustration of the Use of Stochastic Approximation
Louis Guttman, Ruth Guttman · Biometrics · 1959
An ilngenious method, called stochastic approximation, has recelntly been devised by mathematical statisticians for a commonly occurring problem in biological research (and elsewhere). Briefly stated, stochastic approximation is concerned with the regression of a variable y on a variable x, and seeks that value x* for which the regression value of y is some preassigned number y*. The estimation procedure for x* is sequential and distribution-free. Despite its extreme simplicity in application and the wide variety of situations in which it may be useful, the technique has not as yet been taken advanitage of by empirical research workers. One reason for this may be that the existing literature is addressed primarily to professional mathematicialls (a review of the literature is given in [1]). Another reason may be that the mathematical theory itself is not yet complete for relatively small samples. An empirical research project is reported in the present paper in which the technique proved to be highly valuable and economical: it enabled us to arrive relatively quickly at a good estimate of the point of time at which a certain biological effect was attained. The problem was to estimate the time of onset of the action of kinetin on division in Paramecium caudatum where increased rates of cell division have recently been induced by treatment with this substance [2]. We shall explain in detail how stochastic approximation was used to help solve this problem. It is hoped that this example may stimulate the use of this procedure in similar and other varieties of problems. It is also