I have been thinking about this every once and awhile - also i will acknowledge that I havent tried to look up the answer myself yet. I thought, I would throw it out here at TS and see what you have to say.

Say i am running a Bayesian regression model based on MCMC. I end up with a posterior distribution and I grab percentiles from it for my credible intervals. However if I wanted prediction intervals for new values, how do I get those based on the model. In frequentist procedures you tweak the CI formula to get the PIs. I guess a comparable question would also be, in frequentist modeling how would you'd get PIs using bootstrapping?

In both of these settings would you use a modified alpha/critical value of interest? In Bayes is there any philosophical reason for PIs to be different than in frequentist approach, thoughts?

Say i am running a Bayesian regression model based on MCMC. I end up with a posterior distribution and I grab percentiles from it for my credible intervals. However if I wanted prediction intervals for new values, how do I get those based on the model. In frequentist procedures you tweak the CI formula to get the PIs. I guess a comparable question would also be, in frequentist modeling how would you'd get PIs using bootstrapping?

In both of these settings would you use a modified alpha/critical value of interest? In Bayes is there any philosophical reason for PIs to be different than in frequentist approach, thoughts?

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