Credible intervals are an interval within which an unobserved parameter value falls with a particular probability. They are an important concept in Bayesian statistics.
The purpose of credible intervals is to describe and summarise the uncertainty of statistical parameters.
A common way to sharpen the understanding of credibility is the comparison with the term "confidence".
Credibility vs Confidence
Credible intervals can be confused with confidence intervals. However, while their goal is similar, their statistical definition annd meaning is very different. Confidence is rooted in Bayesian inference and is obtained through a complex algorithm full of rarely-tested assumptions and approximations, credibility is fairly straightforward to compute. Credibility means that there is 95% likelihood that a population parameter lies in the designated interval. Many times this interpretation is falsly attributed to confidence (see e.g. Hoekstra, 2014). Confidence, however, works differently: "If we repeat the experiment infinitely many times, 95% of the experiments will capture the population parameter in their confidence intervals."
Finally, the typical interval level for confidence is 95%. While this was the first choice for credibility for some time several authors started to question this and suggested a default credibility of roughly 90% (Kruschke, 2014; McElreath, 2014, 2018).
References
- Hoekstra, R., Morey, R. D., Rouder, J. N., & Wagenmakers, E. J. (2014). Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review, 21(5), 1157-1164.
- Kruschke, J. (2014). Doing bayesian data analysis: A tutorial with r, jags, and stan. Academic Press.
- McElreath, R. (2018). Statistical rethinking: A bayesian course with examples in r and stan. Chapman; Hall/CRC.
