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I had a question regarding how to best perform "sensitivity analysis" on a Beta prior used for a estimating a proportion from a binomially distributed data problem (i.e., beta-binomial problem).

I understand that the shape parameters $\alpha$ and $\beta$ move the Beta to right and left. But how much and on what basis should I change these two parameters and compare their effects on the the posterior 95% credible Intervals (picture below)?

(Note: In the picture below, 'A' parameter denotes 'alpha')

enter image description here

rnorouzian
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  • You can use a uniform prior, which is the same as a Beta(1,1) distribution. Or you can do the empirical Bayes, like [here](https://stats.stackexchange.com/questions/47916/bayesian-batting-average-prior). – dimitriy Dec 12 '17 at 02:38

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