When propriety is improper

Propriety of Posteriors with Improper Priors in Hierarchical Linear Mixed Models

This paper examines necessary and sufficient conditions for the propriety of the posterior distribution in hierarchical linear mixed effects models for a collection of improper prior distributions. In addition to the flat prior for the fixed effects, the collection includes various limiting forms of the invariant gamma distribution for the variance components, including cases considered previou...

When every $P$-flat ideal is flat

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

Improper Priors Are Not Improper

It is well known that improper priors in Bayesian statistics may lead to proper posterior distributions and useful inference procedures. This motivates us to give an elementary introduction to a theoretical frame for statistics that includes improper priors. Axioms that allow improper priors are given by a relaxed version of Kolmogorov’s formulation of probability theory. The theory of conditio...

Two claims about epistemic propriety

This paper has two main parts. In the first part, I argue that prominent moves in two related current debates in epistemology—viz., the debates over classical invariantism and the knowledge first movement—depend on one or the other of two claims about epistemic propriety: (1) Impropriety due to lack of a particular epistemic feature suffices for epistemic impropriety; and (2) Having justificati...

when appropriate statistical analysis is dismissed