Editing Interval estimation (section)

=== Credible intervals ===
{{main|Credible intervals}}

[[File:Prior, Likelihood, Posterior schematic.svg|thumb|Bayesian Distribution: Adjusting a prior distribution to form a posterior probability.]]
As opposed to a confidence interval, a credible interval requires a [[Prior probability|prior]] assumption, modifying the assumption utilizing a [[Bayes factor]], and determining a [[Posterior probability|posterior distribution]]. Utilizing the posterior distribution, one can determine a 100γ% ''probability'' the parameter of interest is included, as opposed to the confidence interval where one can be 100γ% ''confident'' that an estimate is included within an interval.<ref>{{Cite journal |last=Hespanhol |first=Luiz |last2=Vallio |first2=Caio Sain |last3=Costa |first3=Lucíola Menezes |last4=Saragiotto |first4=Bruno T |date=2019-07-01 |title=Understanding and interpreting confidence and credible intervals around effect estimates |url= |journal=Brazilian Journal of Physical Therapy |volume=23 |issue=4 |pages=290–301 |doi=10.1016/j.bjpt.2018.12.006 |issn=1413-3555 |pmc=6630113 |pmid=30638956}}</ref>

:<math>\text{Posterior}\ \propto\ \text{Likelihood} \times \text{Prior}</math>

While a prior assumption is helpful towards providing more data towards building an interval, it removes the objectivity of a confidence interval. A prior will be used to inform a posterior, if unchallenged this prior can lead to incorrect predictions.<ref>{{Cite book |last=Lee |first=Peter M. |title=Bayesian statistics: an introduction |date=2012 |publisher=Wiley |isbn=978-1-118-33257-3 |edition=4. ed., 1. publ |location=Chichester}}</ref>

The credible interval's bounds are variable, unlike the confidence interval. There are multiple methods to determine where the correct upper and lower limits should be located. Common techniques to adjust the bounds of the interval include [[highest posterior density interval]] (HPDI), equal-tailed interval, or choosing the center the interval around the mean.