什麼是決策理論

統計學（statistics）中提出和解決一般決策問題的理論和方法。決策問題可以概述如下︰存在着一組可能的環境條件或可能的初始條件；同時存在若干可供選擇的試驗和對應於這些試驗的可能結果，這些試驗可提供有關環境狀態或初始條件的訊息；還存在若干可供選擇的行動（即決策函數），這些行動與試驗及其結果有關；存在有一組可能的行動後果，每一個可能的行動與每一種環境條件對應某一個確定的後果；問題是在選定試驗和決策函數的條件下估計各種後果出現的可能性，同時，按決策者的意圖或某種規則對一切可能出現的後果給出效用函數（utility function）。所謂問題的最優解（optimal solution）就是選擇最優決策函數（optimal decision function）。最優決策函數使每一個試驗結果對應一個最優行動（optinal act），而最優行動使效用達到極大。同時，問題的最優解還包括選擇一個最優的試驗。亦請參閱cost-benefit analysis、game theory。

decision theory

In statistics and related subfields of philosophy, the theory and method of formulating and solving general decision problems. Such a problem is specified by a set of possible states of the environment or possible initial conditions; a set of available experiments and a set of possible outcomes for each experiment, giving information about the state of affairs preparatory to making a decision; a set of available acts depending on the experiments made and their consequences; and a set of possible consequences of the acts, in which each possible act assigns to each possible initial state some particular consequence. The problem is dealt with by assessing probabilities of consequences conditional on different choices of experiments and acts and by assigning a utility function to the set of consequences according to some scheme of value or preference of the decision maker. An optimal solution consists of an optimal decision function, which assigns to each possible experiment an optimal act that maximizes the utility, or value, and a choice of an optimal experiment. See also cost-benefit analysis, game theory.