Article ID Journal Published Year Pages File Type
397223 International Journal of Approximate Reasoning 2016 24 Pages PDF
Abstract

•A method to quantify prediction uncertainty using belief functions is presented.•The predictive belief function can be approximated using Monte Carlo simulation.•Bayesian posterior distributions are recovered as a special case.•The method is applied to linear regression.

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.

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Physical Sciences and Engineering Computer Science Artificial Intelligence
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