I got the posterior distribution of a parameter from Bayesian analysis. I want to express it as confidence interval. If I plot the empirical cumulative distribution function of the parameter and obtain the 95% interval, will it represent the 95% confidence interval?

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    $\begingroup$ Why not just use the 95% credible interval? The interpretability is often considered more straight forward. The Bayesian credible interval is based on the probability of the parameters given the data. The frequentist confidence interval is based on the probability of the data given some parameters. Here is some discussion of the difference, stats.stackexchange.com/questions/2272/…. $\endgroup$ – OliverFishCode Mar 3 '19 at 21:08
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    $\begingroup$ Why would you do this? This is like having a business class ticket and asking how you can downgrade to economy for free. $\endgroup$ – conjectures Mar 11 at 8:35
  • $\begingroup$ Is this a case of a boss/manager/professor asking you for the 95% confidence interval because that's what she always likes to see around a parameter estimate? $\endgroup$ – Dave Mar 11 at 10:45

No, an X% confidence interval is one where the true value falls within it X% of the time. So a Bayesian credible region can represent a confidence interval only when the frequency coverage matches. It doesn't have to, because the prior can shift the profiles. Best way to check is via simulations.


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