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arXiv · 2112.03129

Bayesian inversion and the Tomita-Takesaki modular group

Luca Giorgetti·Arthur J. Parzygnat·Alessio Ranallo·Benjamin P. Russo
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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.

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Luca Giorgetti, Arthur J. Parzygnat, Alessio Ranallo, Benjamin P. Russo. 2021-12-06. Bayesian inversion and the Tomita-Takesaki modular group. https://doi.org/10.1093/qmath/haad014

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