IMPROPER ADVERTISEMENTS.

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...

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Improper Regular Conditional Distributions

At the bottom of page 1614, we are not precise in the definition of a Borel space. The condition should have read that there is a one-to-one measurable function with measurable inverse between (Ω,B) and (E,E), where E is a Borel subset of the reals and E is the Borel σ-field of subsets of E. After the remaining corrections below, our use of the term “Borel space” conforms with this definition. ...

Proper and Improper Separability

The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of ‘proper’ versus ‘improper’ separability is proposed to mark the distinction. 1 Proper and Improper mixtures In many discussions of the measurement problem in quant...

Improper Filter Reduction

Combinatorial filters have been the subject of increasing interest from the robotics community in recent years. This paper considers automatic reduction of combinatorial filters to a given size, even if that reduction necessitates changes to the filter’s behavior. We introduce an algorithmic problem called improper filter reduction, in which the input is a combinatorial filter F along with an i...