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If we have mean value and 95% confidence interval of a parameter. For example, sensitivity = 0.5, CI = [0.2,0.78](as you can see, it is asymmetric)

How to decide the prior distribution? How to calculate the parameter of chosen prior distribution?

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  • $\begingroup$ In R: code qbeta(c(.025,.5,.975),4.9,5.2) returns $(0.2012826, 0.4841307, 0.7745677).$ $\endgroup$ – BruceET May 30 at 16:32
  • $\begingroup$ @BruceET could you explain what these arguments & output mean in this context? $\endgroup$ – ila May 30 at 16:34
  • $\begingroup$ Distribution $\mathsf{Beta}(4,9,5.2)$ has about 95% of its probability In inteval $(.20, .77)$ and median about $\eta = .48.$ $\endgroup$ – BruceET May 30 at 16:38
  • $\begingroup$ Confidence interval procedures do not use prior distributions: please, then, explain what you are trying to ask. $\endgroup$ – whuber Jun 2 at 12:52