Propagation of Uncertainty in Bayesian Kernel Models: Application to 
Multiple-Step Ahead Forecasting

Quiñonero-Candela, J; Girard, A; Larsen, J; Rasmussen, CE

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Propagation of Uncertainty in Bayesian Kernel Models: Application to Multiple-Step Ahead Forecasting

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Rasmussen, CE
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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http://cogsys.imm.dtu.dk/nnsp2003/
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Citation

Quiñonero-Candela, J., Girard, A., Larsen, J., & Rasmussen, C. (2003). Propagation of Uncertainty in Bayesian Kernel Models: Application to Multiple-Step Ahead Forecasting. In 13th IEEE International Workshop on Neural Networks for Signal Processing (NNSP 2003).

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-DDAE-B

Abstract

The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.