Bo Lindqvist
Department of Mathematical Sciences
Norwegian University of Science and Technology
On improper priors and conditional sampling
It is well known that improper priors in Bayesian statistics may lead
to proper posterior distributions and useful inference procedures. This
motivates the presentation of an elementary theoretical frame for
statistics that includes improper priors, consisting in a relaxation of
Kolmogorov's axioms to allow infinite mass. The theory gives an
alternative to common ad hoc arguments which are not based on an
underlying theory, and it leads to simple explanations of apparent
paradoxes described in the literature. The role of improper
distributions in fiducial statistics and conditional sampling will be
discussed in particular.
This is joint work with Dr. Gunnar Taraldsen, SINTEF, Trondheim,
Norway.
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