The usual priors such as the Jeffreys prior [1] often do not work, because the posterior distribution will not be normalizable and estimates made by minimizing the expected loss will be inadmissible.
[1] In Bayesian probability, the Jeffreys prior is a non-informative (objective) prior distribution for a parameter space; it is proportional to the square root of the determinant of the Fisher information matrix.
Why is this of relevance?
It has the key feature that it is invariant under a change of coordinates for the parameter vector. That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization used to define the Jeffreys prior. This makes it of special interest for use with scale parameters.
Why is this an issue?
Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same theta parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
Ie objects don't spring into existence or disappear or fly around at 400 mph or change direction at 2000 gees.