> Example abridged: a draw from N(phi,1) for unknown phi is 1. Bayesian reasoning with a uniform prior gives an 86% posterior probability that phi > 0 I'm not

> Example abridged: a draw from N(phi,1) for unknown phi is 1. Bayesian reasoning with a uniform prior gives an 86% posterior probability that phi > 0 I'm not sure I see the problem here? If it's counterintuitive, it's only because we treat N(0,1) as the normal distribution, so our true prior is that if we pick a distribution out of a hat we're more likely to have N(0,1) than anything else. Suppose I truly know nothing but what is given in the quote. On the basis of symmetry, I'd have to conclude that P(phi<0) is the same as P(phi>2). If the blogger had phrased this as "86% posterior probability that phi < 2", I don't think it would be so surprising. In fact, the blogger describes this draw as: > after seeing an observation that is statistically indistinguishable from noise. which to me presupposes a great deal of information about what 'noise' is supposed to look like.