Compute distribution of percentile of score

I am modelling the parameters that describe the distribution of my observations. For example, let’s pretend I am modelling the \mu and \sigma of my normally distributed observations. Now, I would like to compute the distribution of the percentile of score; that is, I would like to know the distribution of the proportion of values above a threshold. What is the smart way to do that?

One idea comes to mind. For each combination of parameters in the trace \mu and \sigma, I generate (say) 100 samples from the normal distribution, and I compute the percentile of score. Would that be reasonable?

So the percentile of score is computed on the observations? if so i think your approach sounds quite reasonable.

Yes, I am computing the percentiles on the observations generated by the posterior distribution. I am trying to do something like the Bayesian shift function introduced Here (see strategy 3). I wanted to get some feedback, and it seems it is reasonable :slight_smile: