Independence on Relative Probability Spaces and Consistent Assessments in Game Trees

1997 ◽  
Vol 75 (2) ◽  
pp. 280-313 ◽  
Author(s):  
Elon Kohlberg ◽  
Philip J. Reny
Keyword(s):  
Relative Probability ◽  
Game Trees ◽  
Probability Spaces

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

Statistical Bias Problem in On-Site Surveys: the Severity of the Problem and its Potential for Solution

1975 ◽  
Vol 32 (12) ◽  
pp. 2520-2524
Author(s):  
William F. Sinclair ◽  
R. W. Morley
Keyword(s):  
Fishing Effort ◽  
Recreational Fisheries ◽  
Statistical Bias ◽  
Relative Probability ◽  
Fishing Vessels ◽  
Frequency Of Use ◽  
Unbiased Estimates ◽  
Weighting Procedures ◽  
Use Category

Commercial and recreational fisheries managers often develop catch and effort estimates from information gathered in location or on-site surveys. However, a limited on-site sample cannot produce unbiased estimates of fishing effort or socioeconomic traits of the anglers unless weighting procedures are adopted to account for the varying frequencies of fishing of the fishermen. The corrective procedure involves establishing the relative probability of capturing a fisherman in the sample, then weighting the number of contacts with anglers in each frequency of use category. Unless information on the probability of including particular fishermen and fishing vessels in the sample is available the sample must be drawn with replacement.

On the cohomology equivalence classes for non-singular mappings

1998 ◽  
Vol 18 (6) ◽  
pp. 1385-1397
Author(s):  
ISAAC KORNFELD ◽  
ANDREI KRYGIN
Keyword(s):  
Ergodic Theorem ◽  
Equivalence Classes ◽  
Probability Spaces

The structure of the cohomology equivalence classes for non-singular, not necessarily invertible mappings of probability spaces is studied. In particular, some results of Kochergin and Ornstein–Smorodinsky on the structure of these classes for measure-preserving automorphisms are generalized to the case of non-singular endomorphisms. Our approach is based on Hopf's maximal ergodic theorem and its proof by Garsia.

scholarly journals Structure theorems for game trees

2002 ◽  
Vol 99 (13) ◽  
pp. 9077-9080 ◽  
Author(s):  
S. Govindan ◽  
R. Wilson
Keyword(s):  
Game Trees ◽  
Structure Theorems

THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

2003 ◽  
Vol 06 (03) ◽  
pp. 337-371 ◽  
Author(s):  
NAOFUMI MURAKI
Keyword(s):  
Probability Theory ◽  
Natural Products ◽  
Tensor Product ◽  
Natural Product ◽  
Free Product ◽  
Noncommutative Probability ◽  
Stochastic Independence ◽  
Boolean Product ◽  
Probability Spaces ◽  
Noncommutative Probability Theory

Let [Formula: see text] be the class of all algebraic probability spaces. A "natural product" is, by definition, a map [Formula: see text] which is required to satisfy all the canonical axioms of Ben Ghorbal and Schürmann for "universal product" except for the commutativity axiom. We show that there exist only five natural products, namely tensor product, free product, Boolean product, monotone product and anti-monotone product. This means that, in a sense, there exist only five universal notions of stochastic independence in noncommutative probability theory.

scholarly journals Spatial spread of the West Africa Ebola epidemic

2016 ◽  
Vol 3 (8) ◽  
pp. 160294 ◽  
Author(s):  
Andrew M. Kramer ◽  
J. Tomlin Pulliam ◽  
Laura W. Alexander ◽  
Andrew W. Park ◽  
Pejman Rohani ◽  
...  
Keyword(s):  
West Africa ◽  
Sierra Leone ◽  
Ebola Virus ◽  
Emerging Diseases ◽  
Relative Probability ◽  
Effective Response ◽  
Spatial Spread ◽  
Force Of Infection ◽  
International Border

Controlling Ebola outbreaks and planning an effective response to future emerging diseases are enhanced by understanding the role of geography in transmission. Here we show how epidemic expansion may be predicted by evaluating the relative probability of alternative epidemic paths. We compared multiple candidate models to characterize the spatial network over which the 2013–2015 West Africa epidemic of Ebola virus spread and estimate the effects of geographical covariates on transmission during peak spread. The best model was a generalized gravity model where the probability of transmission between locations depended on distance, population density and international border closures between Guinea, Liberia and Sierra Leone and neighbouring countries. This model out-performed alternative models based on diffusive spread, the force of infection, mobility estimated from cell phone records and other hypothesized patterns of spread. These findings highlight the importance of integrated geography to epidemic expansion and may contribute to identifying both the most vulnerable unaffected areas and locations of maximum intervention value.

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