[rssoconnor]

You can just use the function that is constantly 1 everywhere as your improper prior.

Improper priors are not distributions so they don't need to integrate to 1. You cannot sample from them. However, you can still apply Bayes' rule using improper priors and you usually get a posterior distribution that is proper.

[kgwgk]

Sure.

The point is that you wrote that « you can pick any point […] » and when toth pointed out that « there is always a choice of origin implicit in some way » you replied that « you could use an uninformed improper prior. »

However, it seems that we agree that you cannot pick a point using an uninformed improper prior - and in any method for picking a point there will be an implicit departure from that (improper) uniform distribution.

[rssoconnor]

Oh.

When I said "you can pick any point P", I meant universal quantification, i.e "for all points P", rather than a randomly chosen P.

I did say "choose P", which was pretty bad phrasing on my part.