What does a noninformative prior actually mean?
Abstract The prior distribution is the part of a Bayesian model that most often invites suspicion: “you can make a Bayesian analysis say whatever you want by twisting the prior.” That accusation is sharper than the textbook reply (“priors matter less than you fear, look at the posterior”) suggests, and it is sharper than the casual recipe (“just use a flat prior”) deserves. There are at least five inequivalent answers to “what does an uninformative prior even mean?”, the Jeffreys rule has a beautiful geometric derivation that is rarely spelled out, and improper priors can be perfectly safe or silently wrong depending on the dataset. ...