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1. Bayesian Decision Theory and Stochastic Independence

Author

Philippe Mongin, HEC Paris - Recherche - Hors Laboratoire, Ecole des Hautes Etudes Commerciales (HEC Paris), HEC Research Paper Series, and Haldemann, Antoine

Subjects
FOS: Computer and information sciences, Stochastic independence, History, Property (philosophy), Computer science, Savage, 050905 science studies, lcsh:QA75.5-76.95, History and Philosophy of Science, Probability theory, Computer Science - Computer Science and Game Theory, Representation (mathematics), Probability interpretations, Preference (economics), Probability measure, Bayes estimator, lcsh:Mathematics, 05 social sciences, Probabilistic Independence, JEL: D - Microeconomics/D.D8 - Information, Knowledge, and Uncertainty/D.D8.D81 - Criteria for Decision-Making under Risk and Uncertainty, Stochastic Independence, Subjective expected utility, lcsh:QA1-939, Philosophy, Work (electrical), Mathematical development, J2, [SHS.GESTION]Humanities and Social Sciences/Business administration, lcsh:Electronic computers. Computer science, Bayesian Decision Theory, 0509 other social sciences, [SHS.GESTION] Humanities and Social Sciences/Business administration, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling, Mathematical economics, JEL: D - Microeconomics/D.D8 - Information, Knowledge, and Uncertainty/D.D8.D89 - Other, Computer Science and Game Theory (cs.GT)
Abstract

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory., Comment: In Proceedings TARK 2017, arXiv:1707.08250

Published
2020
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2. Algebraic and topological structures on rational tangles

Author

Seyed M.H. Mansourbeigi, Vida Milani, Hossein Finizadeh, and Poli Paper

Subjects
tangle convergent, Coalgebra, Structure (category theory), Bi-pseudo-module, 010103 numerical & computational mathematics, Interval (mathematics), lcsh:Analysis, Group Hopf algebra, Continued fraction, Topology, 01 natural sciences, Tangle, Interval coalgebra, Incidence algebra, Mathematics::Quantum Algebra, Physical Sciences and Mathematics, Order (group theory), 0101 mathematics, Algebraic number, Mathematics, group Hopf algebra, Computer Sciences, lcsh:Mathematics, lcsh:QA299.6-433, Tangle convergen, bi-pseudo-module, lcsh:QA1-939, Mathematics::Geometric Topology, continued fraction, 010101 applied mathematics, Algebra, incidence algebra, pseudo-tensor product, Pseudo-tensor product, Pseudo-module, pseudo-module, Geometry and Topology, tangle, Locally finite partial order, locally finite partial order, interval coalgebra
Abstract

In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.

Published
2017

3. Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds

Author

Seyed M.H. Mansourbeigi, Vida Milani, Ali Rezaei, and Poli Paper

Subjects
Discrete Morse theory, 06B30, 46L35, 46L85, 55P15, 55U10, Critical points, lcsh:Analysis, C*-algebra, Interpretation (model theory), representation, Mathematics - Geometric Topology, Physical Sciences and Mathematics, FOS: Mathematics, Algebraic Topology (math.AT), Homotopy equivalence, Noncommutative algebraic geometry, Mathematics - Algebraic Topology, Simplicial complex, Handlebody, Circle-valued Morse theory, Morse theory, Mathematics, CW complexes, Computer Sciences, lcsh:Mathematics, lcsh:QA299.6-433, Pseudo-homotopy type, Geometric Topology (math.GT), lcsh:QA1-939, Noncommutative geometry, Homotopy type, Algebra, Poset, Noncommutative CW complex, Morse function, Geometry and Topology, Noncommutative quantum field theory
Abstract

The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. These objects were introduced and studied in [2],[7] and [14]. Some examples to illustrate these geometric information in practice are given. A classification of unital C*-algebras by noncommutative CW complexes and the modified Morse functions on them is the main object of this work., 18 pages

Published
2011