> any value is as plausible as any other as far as I know”
That isn't possible to use as a prior as the uniform distribution from negative to positive infinity is zero everywhere.
That isn't possible to use as a prior as the uniform distribution from negative to positive infinity is zero everywhere.
Failing that, I don't think there are any human usable data sources that could report observations over an infinite interval.
If you don’t think that this is possible that says more about you than about the shortcomings of Bayesian statistics.
As I said, you can define the improper uniform prior solution as the limit of a sequence of solutions corresponding to a sequence of increasingly wider intervals with endpoints that go to +/-infinity.
(And as I said, you can start with a suitably huge region. Say that you want to determine the position of something and use a uniform prior that extends to a distance of 10^27m - a perfectly bounded prior from a mathematical point of view that covers the whole observable universe. If you observe something outside it, it’s not with the prior that you have a problem.)