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.


References in periodicals archive ?
While an abundance of algorithms is now available, a scientifically rigorous theory of uncertainty quantification and statistical decision making for such procedures has not been developed yet.
A sample of paper topics includes measurement and research on stage machinery noise in theater, balance and vibration analysis on an in-line five cylinder engine, stability design of cutting current based on fuzzy control theory, skin color detection using the statistical decision theory, improved design on guardrail used for frequent accident occurring highway section, work principle and application of linear motion unit, teaching in technological institutes, risk decision-making system in manufacture enterprise management, preliminary discussion on training mode of excellence engineer in application oriented university, and study on multimedia education system of technological college.
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.
Statistical decision Real situation Acceptance of zero hypothesis Rejection of zero hypothesis Correct decision Incorrect decision, Zero hypothesis (1-[alpha]).
Regression-based techniques for statistical decision making in single-case designs
Part I covers basic ideas of matrix theory and statistical decision theory, while Part II examines the estimators, their derivations, and the relationships between estimators from Bayesian and non-Bayesian perspectives.
Chapter 18 covers non-parametric tests and the last chapter explains statistical decision theory-an analytical and systematic approach to decision making to arrive at the best possible alternative out of several feasible and viable ones.
Courts should be using more statistical decision rules, not only because they promise greater accuracy, but also because they provide the consistency and transparency to which the law often aspires.
Forward thinking credit and collection managers have begun to appreciate the value that an advanced statistical decision system adds to their bottom line.
He received the Hays Prize after achieving first class marks in Financial Reporting, Financial Management, Management Accounting and Statistical Decision Making subjects.
IK: Could you comment on the relationship between statistical decision theory and game theory?
If the question is simply whether or not to automate, a straightforward design procedure is available by applying standard statistical decision theory to the failure-response task.

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