> Does anyone commonly set their priors to be a distribution? Perhaps a range or actually a normal distribution to represent a prior with uncertainty? Almost e

> Does anyone commonly set their priors to be a distribution? Perhaps a range or actually a normal distribution to represent a prior with uncertainty? Almost everyone does this, and the solution is a posterior probability distribution. Most uses of Bayesian techniques that I'm familiar with are based on Monte Carlo simulations, where priors are drawn from the specified prior distribution, processed in some fashion, and result in samples of the posterior distribution. This is especially helpful when you don't view the problem as having a 'true' single answer with some 'uncertainty' but instead have actual variability in the system, which is described by the posterior distribution. Thinking about it, I'm really not sure in what instance the prior wouldn't be a distribution. It is, by definition, a probability. I suppose you could have a singular value, where the pdf is a delta function, but what's the point of doing the Bayesian inversion or estimation then? If you have a single value with prior p(x) = 0 or 1, you should end up with the posterior p(x|d)=0 or 1. So the simplest case is where the prior is a binary: Say p(x=yes) = 0.6, p(x=no)=0.4. Or something like that. It's not a continuous distribution but it's still a distribution. The sum/integral of all cases has to be 1.