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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Main Authors:	Orakanya Kanjanatarakul, Thierry Denœux, Songsak Sriboonchitta
Format:	Journal
Published:	2018
Subjects:	Computer Science Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84962822288&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55524
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-555242018-09-05T03:06:28Z Prediction of future observations using belief functions: A likelihood-based approach Orakanya Kanjanatarakul Thierry Denœux Songsak Sriboonchitta Computer Science Mathematics © 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. 2018-09-05T02:57:33Z 2018-09-05T02:57:33Z 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/6653943832/55524
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Computer Science Mathematics
spellingShingle	Computer Science Mathematics Orakanya Kanjanatarakul Thierry Denœux Songsak Sriboonchitta Prediction of future observations using belief functions: A likelihood-based approach
description	© 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	Orakanya Kanjanatarakul Thierry Denœux Songsak Sriboonchitta
author_facet	Orakanya Kanjanatarakul Thierry Denœux Songsak Sriboonchitta
author_sort	Orakanya Kanjanatarakul
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	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84962822288&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55524
_version_	1681424521794420736

Prediction of future observations using belief functions: A likelihood-based approach

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