### #70. New paper by Grigorii Melnichenko

Stop the press, here comes an unexpected paper!

Grigorii Melnichenko.

As you may or may not know, broadly speaking there are two main approaches to what a physicist might call non-Kolmogorovian probability. One uses operator-valued probabilities and has led to a quite fruitful field of research called

While the first-mentioned approach has found strong supporters among statisticians, notably Richard Gill (who has a lot of interesting work on `quantum statistics'), I had never seen a paper from the second strand in a Statistics journal (only in Theoretical Physics journals). But there's a first time for everything...

*JMVA*is going to publish yet another fuzzy paper; particularly, a paper on quantum logic.Grigorii Melnichenko.

**Energy discriminant analysis, quantum logic, and fuzzy sets**.*Journal of Multivariate Analysis*, to appear. Update: JMVA**101**(2010), 68-76.As you may or may not know, broadly speaking there are two main approaches to what a physicist might call non-Kolmogorovian probability. One uses operator-valued probabilities and has led to a quite fruitful field of research called

*non-commutative*or*free probability*. The other goes back to work by Birkhoff and von Neumann in the 30's, and uses real-valued probabilities but defined on structures poorer than sigma-algebras (e.g. orthomodular lattices; in the original work, events are defined as closed subspaces of a Hilbert space).While the first-mentioned approach has found strong supporters among statisticians, notably Richard Gill (who has a lot of interesting work on `quantum statistics'), I had never seen a paper from the second strand in a Statistics journal (only in Theoretical Physics journals). But there's a first time for everything...

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