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Its common misinterpretation of a 95% confidence interval to say that that 95% of the time the true value lies within that interval.

However, in Bayesian statistics, the 95% credible interval contains 95% of the probability from the probability density function. And if I repeat the experiment many times, I'm wondering if I can learn something about my prior?

So say I do an experiment to measure a parameter 100 times and I know the true value for each experiment. Then I calculate the credible interval for each experiment. Should expect 95% of the time the credible interval contains the true value? And if its lower, say only 85% of the time the credible interval contains the true parameter, then perhaps the prior is strongly influencing the results and should be changed?

starbuck
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    It sounds like you want to use frequentist methods to test the hypothesis that the actual parameter distribution matches your prior. – Matthew Gunn Jun 22 '17 at 16:20
  • @MatthewGunn Yeah, the reason I naively started thinking about this is that I'd like to know is if there's any kind of tests for a set of Bayesian results that tells you about the performance of the analysis. – starbuck Jun 22 '17 at 16:33
  • My answer to [this question](https://stats.stackexchange.com/questions/96272/methods-for-testing-a-bayesian-methods-software-implementation) provides a frequency property of a Bayesian procedure, but this question's title is much more direct. – jaradniemi Jun 22 '17 at 17:28
  • @jaradniemi Ah thanks! That's basically what I was asking. – starbuck Jun 22 '17 at 18:01
  • @jaradniemi Is there a citation/source that explains the mathematics behind that procedure? I'd like to go read more. – starbuck Jun 22 '17 at 18:04

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