Extended statistical modeling under symmetry; the link toward quantum mechanics

DOI10.1214/009053605000000868zbMath1091.62002arXivquant-ph/0503214OpenAlexW2089829354MaRDI QIDQ2493545

Inge S. Helland

Publication date: 21 June 2006

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0503214

zbMATH Keywords

symmetryquantum theoryHilbert spacemodel reductiongroup representationquantum mechanicscomplete sufficient statisticscomplementaritytransition probabilityGleason's theoremBorn's formula

Mathematics Subject Classification ID

Theory of statistical experiments (62B15) Foundations and philosophical topics in statistics (62A01) Applications of statistics to physics (62P35) Applications of functional analysis in quantum physics (46N50) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (2)

Posterior distribution for negative binomial parameter \(p\) using a group invariant prior ⋮ A statistical framework for modern network science

Cites Work

• Addendum to ``A new approach to causal inference in mortality studies with a sustained exposure period. Application to control of the healthy worker survivor effect
• Quantum probability for probabilists
• Nonrelativistic quantum mechanics as a noncommutative Markov process
• Bayesian inference for causal effects: The role of randomization
• Probability towards 2000. Symposium, Columbia Univ., New York, NY, USA, October 2--6, 1995
• Quantum statistical inference
• Gleason-type derivations of the quantum probability rule for generalized measurements
• Causal inference for complex longitudinal data: the continuous case.
• What is a statistical model? (With comments and rejoinder).
• Quantum probability from decision theory?
• Noncommuting observables in quantum detection and estimation theory
• Fisher information in quantum statistics
• Causal Inference Without Counterfactuals
• On Quantum Statistical Inference
• Quantum theory of probability and decisions
• A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect
• QUANTUM PROBABILITIES AND PARADOXES OF THE QUANTUM CENTURY
• Unknown quantum states: The quantum de Finetti representation
• Lectures on Quantum Theory
• Can Quantum-Mechanical Description of Physical Reality be Considered Complete?
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Extended statistical modeling under symmetry; the link toward quantum mechanics