Posterior for noninformative prior

May I ask that do we always have closed form of posterior distribution for common likelihood (eg. Normal, Lognormal, Logistic etc) when we use noninformative priors (eg, unif(a,b) with small a and large b or N(0, sigma^2) where sigma is pretty large).

@stan_beginer, thanks for posting.

I’m not exactly sure what you mean… you can write models with noninformative priors in Stan, but you could easily end up with improper posterior distributions (integral over the parameters is divergent or infinity or improper).

The simplest thing I can think of…

data { } // no data
parameters { 
  real theta;
model { } 

This puts an improper prior on theta which is uniform from -infinity to +infinity.

Using Stan’s algorithms for MCMC and optimization will both fail for this model for good reason.

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I think that when you use Jeffrey’s priors, then you have an analytical solution of the posterior, but those are really hard to find, and then you have to find the posterior 's solution that is hard as well. Miggon and Fonseca have a lot of work with those priors.

Maybe that helps too.