In Bayesian statistics, what is a credible interval?

In Bayesian statistics, what is a credible interval?

• A. Credible interval
• B. Confidence interval
• C. Prediction interval
• D. Posterior interval

Answer: (A)

In Bayesian statistics, a credible interval is a range of parameter values that contains a specified portion of the posterior distribution after observing the data. After updating your prior beliefs with the data through Bayes’ theorem, the posterior distribution expresses how plausible different parameter values are given what you’ve observed. A 95% credible interval means there is a 0.95 posterior probability that the true parameter lies inside that interval, given the data and the prior. This interval can be formed as equal-tailed (cutting off 2.5% from each tail) or as a highest posterior density interval, which is the narrowest interval containing 95% of the posterior mass. The interpretation is about the parameter itself, conditional on the data and prior, rather than about long-run frequency properties of a procedure. While you might hear “posterior interval,” the standard term for this uncertainty range in Bayesian practice is a credible interval.

In Bayesian statistics, a credible interval is a range of parameter values that contains a specified portion of the posterior distribution after observing the data. After updating your prior beliefs with the data through Bayes’ theorem, the posterior distribution expresses how plausible different parameter values are given what you’ve observed. A 95% credible interval means there is a 0.95 posterior probability that the true parameter lies inside that interval, given the data and the prior. This interval can be formed as equal-tailed (cutting off 2.5% from each tail) or as a highest posterior density interval, which is the narrowest interval containing 95% of the posterior mass. The interpretation is about the parameter itself, conditional on the data and prior, rather than about long-run frequency properties of a procedure. While you might hear “posterior interval,” the standard term for this uncertainty range in Bayesian practice is a credible interval.