决策理论(decision theory)

统计学（statistics）中提出和解决一般决策问题的理论和方法。决策问题可以概述如下︰存在着一组可能的环境条件或可能的初始条件；同时存在若干可供选择的试验和对应於这些试验的可能结果，这些试验可提供有关环境状态或初始条件的讯息；还存在若干可供选择的行动（即决策函数），这些行动与试验及其结果有关；存在有一组可能的行动後果，每一个可能的行动与每一种环境条件对应某一个确定的後果；问题是在选定试验和决策函数的条件下估计各种後果出现的可能性，同时，按决策者的意图或某种规则对一切可能出现的後果给出效用函数（utility function）。所谓问题的最优解（optimal solution）就是选择最优决策函数（optimal decision function）。最优决策函数使每一个试验结果对应一个最优行动（optinal act），而最优行动使效用达到极大。同时，问题的最优解还包括选择一个最优的试验。亦请参阅cost-benefit analysis、game theory。

English version：

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.