william's blog | 2012-02-04 11:47:14 +0000 =========================================== A philosophical question ------------------------ Date: October 7, 2008 3:25am Author: William Morgan Labels: stats URL: http://masanjin.net/blog/old19.txt Is there really a difference between saying, "I don't know anything, a priori, about the parameters of this distribution", and using a uniform prior? What about, "I don't know anything about that value" versus "As far as I'm concerned, every possibility for that value is equally likely"? Replies -------- Brendan, on October 12, 2008 1:17am: ["| I think so.\n", "| \n", "| Sometimes I really have no clue what true value is, but a uniform prior is too\n", "| assertive.\n", "| \n", "| And what about uniform priors over a real-valued parameter? (You can do that\n", "| if you're happy with an improper prior; it often still works after the bayes\n", "| update even.) Do I really think theta=1million is just as likely as theta=25?\n", "| There are lots of situations where I would say \"no\", but I would be unwilling\n", "| to say the exact ratio between their prior probabilities.\n", "| \n", "| On the other hand, if all a prior is is a placeholder before you update it\n", "| with a data likelihood, then it doesn't matter. I think it's hard to call\n", "| this \"bayesian\" though.\n", "| \n"] William, on October 14, 2008 6:41pm: ["| I think the answer is no.\n", "| \n", "| You're talking about a case where you DO have an idea about what the prior\n", "| probabilities are, you just don't know the particular shape. In that case, a\n", "| uniform prior is \"too assertive\", but only because it forces a particular\n", "| distribution.\n", "| \n", "| I'm talking about the case where you say something like \"I don't know anything\n", "| about this, and I refuse to commit to any prior belief at all\". That's what I\n", "| don't see as any different from a uniform prior.\n", "| \n", "| And maybe this is nit-picking but you only have to resort to improper priors\n", "| if your real-value parameter is unbounded. :)\n", "| \n"] This delicious text version served up by Whisper .