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.
- Choosing the interval where the probability of being below the interval is as likely as being above it. This interval will include the median.
- Assuming 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.
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