On 29 Mar 2004 02:32:50 GMT, [EMAIL PROTECTED] (Radford Neal) wrote:
>Ah! But regardless of whether you think the DENSITY approximates 1/x >"pretty well", the DISTRIBUTION doesn't. Sure, but for a prior, it's the density that matters. >Far from the distribution for log(x) being uniform over a region >around zero, it's highly biased in the downwards direction, and has >less than a 1% chance of taking on a value greater than zero (ie, a >value for x greater than one). So it's far too vague in one >direction, and not vague enough in the other. I plotted the density (which I think is more relevant than the quantiles), and I see your point. The density of log(x) is only approximately uniform up to around log(x) = 3, i.e. x = 20. >If you want a "vague" prior centered around 1, you'd do better >with gamma(0.1,0.00001): > > > summary(rgamma(100000,0.1,0.00001)) > Min. 1st Qu. Median Mean 3rd Qu. Max. > 1.358e-48 5.960e-02 5.982e+01 9.911e+03 3.448e+03 7.583e+05 That one doesn't have a very flat density for log(x) at all, because of the large shape parameter. I'd say you're better shrinking the beta parameter until you get the coverage you need. For example, (alpha,beta)=(0.001,0.00000001) is pretty flat up to log(x)=15, or x=3000000. But you might not like the median, which R reports as > qgamma(0.5,0.001,0.00000001) [1] 5.244206e-294 >Better yet, if you want a distribution for log(x) that's uniform over >several orders of magnitude around zero, I'd recommend using the >uniform distribution extending for several orders of magnitude around >zero. Or you could use a log normal distribution. I agree those would be fine, though if you were making use of conjugacy, they wouldn't be so convenient. But if that were the case, you could just go to alpha=0, beta=0. Duncan Murdoch . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
