Advanced search
1 file | 697.93 KB

A behavioural justification for using sensitivity analysis in imprecise multinomial processes

Jasper De Bock (UGent) and Gert De Cooman (UGent)
Author
Organization
Abstract
We consider two fundamentally different ways of defining an imprecise-probabilistic multinomial process. On the one hand, we have the so-called sensitivity analysis approach. The corresponding imprecise-probabilistic joint model is defined as the lower envelope of joint models of precise multinomial processes, each of which has a different marginal model taken from some closed and convex set of candidate marginal models. For finite subsets of variables in this process, this corresponds to using Walley's so-called type-2 product of identically distributed variables. On the other hand, we consider a behavioural approach, defining an imprecise multinomial process by imposing exchangeability and either forward irrelevance or epistemic independence. Our main result is that both approaches lead to the exact same imprecise multinomial process. This fairly technical result has an important philosophical consequence as well: it provides the sensitivity analysis approach and the related type-2 product with a behavioural justification. We compare our justification favourably with a previous attempt by Cozman and explain how it fits into the more general problem of providing a behavioural justification for so-called strongly independent models, or equivalently, for using lower envelopes of stochastically independent models. (C) 2018 Elsevier Inc. All rights reserved.
Keywords
LOWER PREVISIONS, Imprecise multinomial processes, Sensitivity analysis, Exchangeability, Type-2 product, Forward irrelevance, Epistemic independence

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 697.93 KB

Citation

Please use this url to cite or link to this publication:

Chicago
De Bock, Jasper, and Gert De Cooman. 2018. “A Behavioural Justification for Using Sensitivity Analysis in Imprecise Multinomial Processes.” Journal of Mathematical Analysis and Applications 468 (1): 513–546.
APA
De Bock, Jasper, & De Cooman, G. (2018). A behavioural justification for using sensitivity analysis in imprecise multinomial processes. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 468(1), 513–546.
Vancouver
1.
De Bock J, De Cooman G. A behavioural justification for using sensitivity analysis in imprecise multinomial processes. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. San diego: Academic Press Inc Elsevier Science; 2018;468(1):513–46.
MLA
De Bock, Jasper, and Gert De Cooman. “A Behavioural Justification for Using Sensitivity Analysis in Imprecise Multinomial Processes.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 468.1 (2018): 513–546. Print.
@article{8575340,
  abstract     = {We consider two fundamentally different ways of defining an imprecise-probabilistic multinomial process. On the one hand, we have the so-called sensitivity analysis approach. The corresponding imprecise-probabilistic joint model is defined as the lower envelope of joint models of precise multinomial processes, each of which has a different marginal model taken from some closed and convex set of candidate marginal models. For finite subsets of variables in this process, this corresponds to using Walley's so-called type-2 product of identically distributed variables. On the other hand, we consider a behavioural approach, defining an imprecise multinomial process by imposing exchangeability and either forward irrelevance or epistemic independence. Our main result is that both approaches lead to the exact same imprecise multinomial process. This fairly technical result has an important philosophical consequence as well: it provides the sensitivity analysis approach and the related type-2 product with a behavioural justification. We compare our justification favourably with a previous attempt by Cozman and explain how it fits into the more general problem of providing a behavioural justification for so-called strongly independent models, or equivalently, for using lower envelopes of stochastically independent models. (C) 2018 Elsevier Inc. All rights reserved.},
  author       = {De Bock, Jasper and De Cooman, Gert},
  issn         = {0022-247X},
  journal      = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
  language     = {eng},
  number       = {1},
  pages        = {513--546},
  publisher    = {Academic Press Inc Elsevier Science},
  title        = {A behavioural justification for using sensitivity analysis in imprecise multinomial processes},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2018.08.029},
  volume       = {468},
  year         = {2018},
}

Altmetric
View in Altmetric
Web of Science
Times cited: