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Multistep Prediction using Point-Cloud Approximation of Continuous Belief Functions

We consider the problem of quantifying prediction uncertainty in the Dempster-Shafer framework. Our approach assumes a parametric statistical model relating the variable of interest, the parameter and a pivotal random variable with known probability distribution. A predictive belief function is computed using this model and a belief function defined in the parameter space. In the case of multistep prediction, the quantity to be predicted is a vector, and the predictive belief function is defined in a multidimensional space, making its representation and manipulation difficult. To address this issue, we propose to approximate the focal sets of belief functions using point clouds, which allows us to approximate the belief and plausibility of arbitrary events with any accuracy. As an illustration, the approach is applied to the case of a first-order autoregressive process.