Prediction of future observations using belief functions: A likelihood-based approach
© 2015 Elsevier Inc. All rights reserved. We study a new approach to statistical prediction in the Dempster-Shafer framework. Given a parametric model, the random variable to be predicted is expressed as a function of the parameter and a pivotal random variable. A consonant belief function in the pa...
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th-cmuir.6653943832-419152017-09-28T04:24:08Z Prediction of future observations using belief functions: A likelihood-based approach Kanjanatarakul O. Denœux T. Sriboonchitta S. © 2015 Elsevier Inc. All rights reserved. We study a new approach to statistical prediction in the Dempster-Shafer framework. Given a parametric model, the random variable to be predicted is expressed as a function of the parameter and a pivotal random variable. A consonant belief function in the parameter space is constructed from the likelihood function, and combined with the pivotal distribution to yield a predictive belief function that quantifies the uncertainty about the future data. The method boils down to Bayesian prediction when a probabilistic prior is available. The asymptotic consistency of the method is established in the iid case, under some assumptions. The predictive belief function can be approximated to any desired accuracy using Monte Carlo simulation and nonlinear optimization. As an illustration, the method is applied to multiple linear regression. 2017-09-28T04:24:08Z 2017-09-28T04:24:08Z 2016-05-01 Journal 0888613X 2-s2.0-84962822288 10.1016/j.ijar.2015.12.004 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84962822288&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41915 |
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© 2015 Elsevier Inc. All rights reserved. We study a new approach to statistical prediction in the Dempster-Shafer framework. Given a parametric model, the random variable to be predicted is expressed as a function of the parameter and a pivotal random variable. A consonant belief function in the parameter space is constructed from the likelihood function, and combined with the pivotal distribution to yield a predictive belief function that quantifies the uncertainty about the future data. The method boils down to Bayesian prediction when a probabilistic prior is available. The asymptotic consistency of the method is established in the iid case, under some assumptions. The predictive belief function can be approximated to any desired accuracy using Monte Carlo simulation and nonlinear optimization. As an illustration, the method is applied to multiple linear regression. |
| format |
Journal |
| author |
Kanjanatarakul O. Denœux T. Sriboonchitta S. |
| spellingShingle |
Kanjanatarakul O. Denœux T. Sriboonchitta S. Prediction of future observations using belief functions: A likelihood-based approach |
| author_facet |
Kanjanatarakul O. Denœux T. Sriboonchitta S. |
| author_sort |
Kanjanatarakul O. |
| title |
Prediction of future observations using belief functions: A likelihood-based approach |
| title_short |
Prediction of future observations using belief functions: A likelihood-based approach |
| title_full |
Prediction of future observations using belief functions: A likelihood-based approach |
| title_fullStr |
Prediction of future observations using belief functions: A likelihood-based approach |
| title_full_unstemmed |
Prediction of future observations using belief functions: A likelihood-based approach |
| title_sort |
prediction of future observations using belief functions: a likelihood-based approach |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84962822288&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/41915 |
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1681422090721296384 |