paulgstf
commented
4 years ago I mostly agree @aiod01 , yes, the tradeoff is avoiding to decide exactly how wide the prior distribution should be and exactly where it should be centered, at the cost of no longer having a "real" prior distribution. But in fact more and more improper priors are falling out of use. In part this is because they aren't supported by the standard software packages (jags, stan), and in part because without being careful one can end up specifying an improper prior that doesn't give a proper posterior.
tom-hc-park
I would like to hear some your comment about improper prior distribution.
Sometimes we start from a non informative prior distribution when we are so unclear about our guessing of the parameters' distribution.
improper prior distribution is, from my understanding, a further exaggeration of our unclearness about the distribution of the parameters of our interest.
The fact that we sometimes use improper prior seems to imply to me that sometimes, the best non-informative prior distribution is still supposing some assumptions that we really do not want to presume. In order to give up the dangerous assumptions which we prefer to avoid, we are willing to pay the price, that is, one of the property of probability function that Lebesgue integration of the function over the support of our random variable equals to one?