Conditional Expectations

1997 ◽  
pp. 443-456
Author(s):  
Bert Fristedt ◽  
Lawrence Gray
Keyword(s):  
Conditional Expectations

scholarly journals Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 45
Author(s):  
Emilio Gómez-Déniz ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Structural Model ◽  
Medical Expenditure Panel Survey ◽  
Health Care Use ◽  
Medical Expenditure ◽  
Panel Survey ◽  
Conditional Distributions ◽  
Conditional Dependence ◽  
Outpatient Visits ◽  
Conditional Expectations ◽  
The U.S

We jointly model amount of expenditure for outpatient visits and number of outpatient visits by considering both dependence and simultaneity by proposing a bivariate structural model that describes both variables, specified in terms of their conditional distributions. For that reason, we assume that the conditional expectation of expenditure for outpatient visits with respect to the number of outpatient visits and also, the number of outpatient visits expectation with respect to the expenditure for outpatient visits is related by taking a linear relationship for these conditional expectations. Furthermore, one of the conditional distributions obtained in our study is used to derive Bayesian premiums which take into account both the number of claims and the size of the correspondent claims. Our proposal is illustrated with a numerical example based on data of health care use taken from Medical Expenditure Panel Survey (MEPS), conducted by the U.S. Agency of Health Research and Quality.

scholarly journals Approximate Tensorization of the Relative Entropy for Noncommuting Conditional Expectations

2021 ◽  
Author(s):  
Ivan Bardet ◽  
Ángela Capel ◽  
Cambyse Rouzé
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Logarithmic Sobolev Inequality ◽  
Spin Systems ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Finite Dimensional ◽  
Lattice Spin ◽  
Lattice Spin Systems ◽  
Conditional Expectations

AbstractIn this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. This generalisation, referred to as approximate tensorization of the relative entropy, consists in a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

scholarly journals Conditioning using conditional expectations: the Borel–Kolmogorov Paradox

Synthese ◽  
2016 ◽  
Vol 194 (7) ◽  
pp. 2595-2630 ◽  
Author(s):  
Z. Gyenis ◽  
G. Hofer-Szabó ◽  
M. Rédei
Keyword(s):  
Conditional Expectations

scholarly journals Induced Class Functions are Conditional Expectations

1989 ◽  
Vol 10 (3) ◽  
pp. 293-296 ◽  
Author(s):  
Jonathan D.H. Smith
Keyword(s):  
Conditional Expectations

Conditional Expectations

1994 ◽  
pp. 440-483
Author(s):  
J. Hoffmann-Jørgensen
Keyword(s):  
Conditional Expectations

scholarly journals Inclusions of ternary rings of operators and conditional expectations

2013 ◽  
Vol 155 (3) ◽  
pp. 475-482 ◽  
Author(s):  
PEKKA SALMI ◽  
ADAM SKALSKI
Keyword(s):  
Conditional Expectation ◽  
Ternary Ring ◽  
Conditional Expectations

AbstractIt is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P: T → X then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned.

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