I’m sympathetic to the mixture of simple priors approach and value simplicity a great deal. However, I don’t think that the uniform prior up to an arbitrary end point is the simplest as your comment appears to suggest. e.g. I don’t see how it is simpler than an exponential distribution with an arbitrary mean (which is the max entropy prior over R+ conditional on a finite mean). I’m not sure if there is a max entropy prior over R+ without the finite mean assumption, but 1/x^2 looks right to me for that.
Also, re having a distribution that increases over a fixed time interval giving a peak at the end, I agree that this kind of thing is simple, but note that since we are actually very uncertain over when that interval ends, that peak gets very smeared out. Enough so that I don’t think there is a peak at the end at all when the distribution is denominated in years (rather than centiles through human history or something). That said, it could turn into a peak in the middle, depending on the nature of one’s distribution over durations.
I’m sympathetic to the mixture of simple priors approach and value simplicity a great deal. However, I don’t think that the uniform prior up to an arbitrary end point is the simplest as your comment appears to suggest. e.g. I don’t see how it is simpler than an exponential distribution with an arbitrary mean (which is the max entropy prior over R+ conditional on a finite mean). I’m not sure if there is a max entropy prior over R+ without the finite mean assumption, but 1/x^2 looks right to me for that.
Also, re having a distribution that increases over a fixed time interval giving a peak at the end, I agree that this kind of thing is simple, but note that since we are actually very uncertain over when that interval ends, that peak gets very smeared out. Enough so that I don’t think there is a peak at the end at all when the distribution is denominated in years (rather than centiles through human history or something). That said, it could turn into a peak in the middle, depending on the nature of one’s distribution over durations.