45 citations · 110 across the 15 of their papers we have counts for
11 papers · 1 filter
Fiducial and Posterior Sampling
Gunnar Taraldsen, Bo H. Lindqvist
The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is here generalized. For this the underlying probability space of Kolmogo…
Conditional probability and improper priors
Gunnar Taraldsen, Bo H. Lindqvist
The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in th…
Fiducial Symmetry in Action
Gunnar Taraldsen
Symmetry is key in classical and modern physics. A striking example is conservation of energy as a consequence of time-shift invariance from Noether's theorem. Symmetry is likewise…
Statistics with improper posteriors
Gunnar Taraldsen, Jarle Tufto, Bo H. Lindqvist
In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated…
Optimal Learning from the Doob-Dynkin lemma
Gunnar Taraldsen
The Doob-Dynkin Lemma gives conditions on two functions and that ensure existence of a function so that . This communication proves different versions of…
On the proper treatment of improper distributions
Bo H. Lindqvist, Gunnar Taraldsen
The axiomatic foundation of probability theory presented by Kolmogorov has been the basis of modern theory for probability and statistics. In certain applications it is, however, n…
Conditional fiducial models
Gunnar Taraldsen, Bo H. Lindqvist
The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particula…
Improper posteriors are not improper
Gunnar Taraldsen, Jarle Tufto, Bo H. Lindqvist
In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional expectation. In 1955 Renyi fomulated a new axiomatic theory for probability motivated…
Image transformations on locally compact spaces
Gunnar Taraldsen
An image is here defined to be a set which is either open or closed and an image transformation is structure preserving in the following sense: It corresponds to an algebra homomor…
Nonlinear probability. A theory with incompatible stochastic variables
Gunnar Taraldsen
In 1991 J.F. Aarnes introduced the concept of quasi-measures in a compact topological space and established the connection between quasi-states on and quasi-measures in…
Fiducial theory and optimal inference
Gunnar Taraldsen, Bo Henry Lindqvist
It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof do…