Forecasting using belief functions: An application to marketing econometrics

• Main Authors: Orakanya Kanjanatarakul, Songsak Sriboonchitta, Thierry Denœux
• Format: Journal
• Published: 2018
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84899915661&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/45683
• Institution: Chiang Mai University

A method is proposed to quantify uncertainty on statistical forecasts using the formalism of belief functions. The approach is based on two steps. In the estimation step, a belief function on the parameter space is constructed from the normalized likelihood given the observed data. In the prediction step, the variable Y to be forecasted is written as a function of the parameter θ and an auxiliary random variable Z with known distribution not depending on the parameter, a model initially proposed by Dempster for statistical inference. Propagating beliefs about θ and Z through this model yields a predictive belief function on Y. The method is demonstrated on the problem of forecasting innovation diffusion using the Bass model, yielding a belief function on the number of adopters of an innovation in some future time period, based on past adoption data. © 2014 Elsevier B.V. All rights reserved.