Nice examples and discussion here at Andrew Gelman’s blog.
Cool huh? Well, I can imagine a lot of people saying that they want to see where the 95% CI lies, not just some fuzziness stretching out to infinity. I agree with that but for a casual statistics user this could be an engaging starting point. Also, don’t forget that clients in business and politics (1) hate uncertainty yet (2) love pretty graphs… so these could be useful.
There’s a practical stumbling block for a lot of users, as I said in a comment on the original blog. To get all the little fuzzy lines out, you need to know not just the standard errors of all the parameters but (and this bit is usually NOT produced by your favourite stats software, unless you know how to calculate it or dig it out of the computer’s memory) the covariances too. A really easy way of getting these lines would be non-parametric bootstrap, which avoids the covariance matrix calculations entirely, but of course it is not applicable in every situation, and sometimes it causes more trouble to program than it saves. Gelman mentions using Bayesian methods, which similarly give you a multitude of plausible answers that you can plot as lines straight away without working out the covariance matrix.