The highest-density 90% credible interval of a posterior probability distribution
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In Bayesian statistics, a credible interval is an interval used to characterize a probability distribution. It is defined such that an unobserved parameter value has a particular probability to fall within it. For example, in an experiment that determines the distribution of possible values of the parameter , if the probability that lies between 35 and 45 is 0.95, then is a 95% credible interval.
Credible intervals are typically used to characterize posterior probability distributions or predictive probability distributions.[1] The generalisation to multivariate problems is the credible region.
Credible intervals are a Bayesian analog to confidence intervals in frequentist statistics.[2] The two concepts arise from different philosophies:[3] 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. Also, Bayesian credible intervals use (and indeed, require) knowledge of the situation-specific prior distribution, while the frequentist confidence intervals do not.
^Edwards, Ward; Lindman, Harold; Savage, Leonard J. (1963). "Bayesian statistical inference in psychological research". Psychological Review. 70 (3): 193–242. doi:10.1037/h0044139.
^Lee, P.M. (1997) Bayesian Statistics: An Introduction, Arnold. ISBN 0-340-67785-6
^VanderPlas, Jake. "Frequentism and Bayesianism III: Confidence, Credibility, and why Frequentism and Science do not Mix | Pythonic Perambulations". jakevdp.github.io.
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variables are measured on an interval or ratio scale. Other correlation coefficients or analyses are used when variables are not interval or ratio, or when they...
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approximately independent and normal with a mean of 0. Therefore, a confidence interval can be constructed by dividing a selected z-score by n {\displaystyle {\sqrt...
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