Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [65 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01294271
Contributor : Thierry Denoeux Connect in order to contact the contributor
Submitted on : Tuesday, March 29, 2016 - 5:07:12 AM
Last modification on : Wednesday, July 4, 2018 - 4:44:02 PM
Long-term archiving on: : Monday, November 14, 2016 - 7:22:24 AM

File

ijar_belief2014_v3.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Orakanya Kanjanatarakul, Thierry Denoeux, Songsak Sriboonchitta. Prediction of future observations using belief functions: A likelihood-based approach. International Journal of Approximate Reasoning, Elsevier, 2016, 72, pp.71-94. ⟨10.1016/j.ijar.2015.12.004⟩. ⟨hal-01294271⟩

Share

Metrics

Record views

324

Files downloads

559