Statistical Decision

Statistical Decision

 

Statistical decisions are decisions made on the basis of observations of a phenomenon that obeys probabilistic laws that are not completely known (seePROBABILITY) .

As an example, let us consider the disinfection of water by chlorination. The amount of chlorine to be added should depend on the average number θ of bacteria per unit volume. The value of θ, however, is not known and is estimated from the results X1, X2,....Xn of a computation of the number of bacteria in n independently selected unit volumes of water. In the simplest model it is assumed that Xi, for i = 1,...,n, has a Poisson distribution with the unknown mean (mathematical expectation) θ. The statistical decision as to the amount of chlorine to be added will therefore be a function of a statistical estimator θ* of the parameter θ. In selecting θ* there must be taken into account the undesirable consequences of both an underestimate of θ (insufficient disinfection of the water) and an overestimate of θ (worsening of the taste of the water owing to excessive chlorination).

Statistical decision theory provides a precise mathematical formulation of the concepts pertaining to statistical decisions and to methods of comparing statistical decisions.

IU. V. PROKHOROV

References in periodicals archive ?
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The data analysis consisted of obtaining the percentage of errors in the statistical decision using the t-test of the independent groups (according with the homocedasticity condition) for the 5000 comparisons in the 33 conditions for both scenarios, the nonparametric Mann-Whitney U-test, Yuen-Welch's t-test (Wilcox, 2005) and the comparison of the confidence intervals of means and medians in the seven used procedures.
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