Bayesian inversion and the Tomita–Takesaki modular group

by Luca Giorgetti, Arthur Parzygnat, Alessio Ranallo, Benjamin P Russo

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Journal Name

The Quarterly Journal of Mathematics

Publication Date

March, 2023

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Abstract

We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional C∗-algebras.

Bayesian inversion and the Tomita–Takesaki modular group

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