Using second-order probabilities to make maximum entropy approach to copulas more reasonable

© 2014 by the Mathematical Association of Thailand. All rights reserved. Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is...

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Main Authors: Hung T. Nguyen, Vladik Kreinovichz, Berlin Wu
Format: Journal
Published: 2018
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84907253524&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45640
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-456402018-01-24T06:14:26Z Using second-order probabilities to make maximum entropy approach to copulas more reasonable Hung T. Nguyen Vladik Kreinovichz Berlin Wu © 2014 by the Mathematical Association of Thailand. All rights reserved. Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the largest entropy. However, in some cases, the maximum entropy approach leads to an unreasonable selection – e.g., even if we know that the two random variables are positively correlated, the maximum entropy approach completely ignores this information. In this paper, we show how to properly modify the maximum entropy approach so that it will lead to more reasonable results: by applying this approach not to the probabilities themselves, but to “second order” probabilities – i.e., probabilities of different probability distributions. 2018-01-24T06:14:26Z 2018-01-24T06:14:26Z 2014-01-01 Journal 16860209 2-s2.0-84907253524 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84907253524&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45640
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
description © 2014 by the Mathematical Association of Thailand. All rights reserved. Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the largest entropy. However, in some cases, the maximum entropy approach leads to an unreasonable selection – e.g., even if we know that the two random variables are positively correlated, the maximum entropy approach completely ignores this information. In this paper, we show how to properly modify the maximum entropy approach so that it will lead to more reasonable results: by applying this approach not to the probabilities themselves, but to “second order” probabilities – i.e., probabilities of different probability distributions.
format Journal
author Hung T. Nguyen
Vladik Kreinovichz
Berlin Wu
spellingShingle Hung T. Nguyen
Vladik Kreinovichz
Berlin Wu
Using second-order probabilities to make maximum entropy approach to copulas more reasonable
author_facet Hung T. Nguyen
Vladik Kreinovichz
Berlin Wu
author_sort Hung T. Nguyen
title Using second-order probabilities to make maximum entropy approach to copulas more reasonable
title_short Using second-order probabilities to make maximum entropy approach to copulas more reasonable
title_full Using second-order probabilities to make maximum entropy approach to copulas more reasonable
title_fullStr Using second-order probabilities to make maximum entropy approach to copulas more reasonable
title_full_unstemmed Using second-order probabilities to make maximum entropy approach to copulas more reasonable
title_sort using second-order probabilities to make maximum entropy approach to copulas more reasonable
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84907253524&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45640
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