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A credal set is a set of probability distributions〔Levi, I. (1980). ''The Enterprise of Knowledge''. MIT Press, Cambridge, Massachusetts. 〕 or, equivalently, a set of probability measures. A credal set is often assumed or constructed to be a closed convex set. It is intended to express uncertainty or doubt about the probability model that should be used, or to convey the beliefs of a Bayesian agent about the possible states of the world.〔Cozman, F. (1999). (Theory of Sets of Probabilities (and related models) in a Nutshell ).〕 Let denote a categorical variable, a probability mass function over , and a credal set over . If is convex, the credal set can be equivalently described by its extreme points . The expectation for a function of with respect to the credal set can be characterised only by its lower and upper bounds. For the lower bound, : Notably, such an inference problem can be equivalently obtained by considering only the extreme points of the credal set. It is easy to see that a credal set over a Boolean variable cannot have more than two vertices, while no bounds can be provided for credal sets over variables with three or more values. ==See also== * imprecise probability * Dempster–Shafer theory * probability box * robust Bayes analysis * upper and lower probabilities 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「credal set」の詳細全文を読む スポンサード リンク
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