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In Bayesian statistics, a credible interval is an interval in the domain of a posterior probability distribution or predictive distribution used for interval estimation.〔Edwards, Ward, Lindman, Harold, Savage, Leonard J. (1963) "Bayesian statistical inference in psychological research". ''Psychological Review'', 70, 193-242〕 The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals in frequentist statistics,〔Lee, P.M. (1997) ''Bayesian Statistics: An Introduction'', Arnold. ISBN 0-340-67785-6〕 although they differ on a philosophical basis; Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value. For example, in an experiment that determines the uncertainty distribution of parameter , if the probability that lies between 35 and 45 is 0.95, then is a 95% credible interval. ==Choosing a credible interval== Credible intervals are not unique on a posterior distribution. Methods for defining a suitable credible interval include: *Choosing the narrowest interval, which for a unimodal distribution will involve choosing those values of highest probability density including the mode. This is sometimes called the highest posterior density interval. *Choosing the interval where the probability of being below the interval is as likely as being above it. This interval will include the median. This is sometimes called the equal-tailed interval. *Assuming that the mean exists, choosing the interval for which the mean is the central point. It is possible to frame the choice of a credible interval within decision theory and, in that context, an optimal interval will always be a highest probability density set.〔O'Hagan, A. (1994) ''Kendall's Advanced Theory of Statistics, Vol 2B, Bayesian Inference'', Section 2.51. Arnold, ISBN 0-340-52922-9〕 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「credible interval」の詳細全文を読む スポンサード リンク
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