relation: https://eprints.gla.ac.uk/3719/ title: Gaussian processes: prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series creator: Girard, A. creator: Murray-Smith, R. subject: QA75 Electronic computers. Computer science description: With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (<i>Gaussian</i> <i>approximation</i>). We show how, depending on the form of the covariance function of the process, we can evaluate these moments exactly or approximately (within a Taylor approximation of the covariance function). We apply our results to the iterative multiple-step ahead prediction of non-linear dynamic systems with propagation of the uncertainty as we predict ahead in time. Finally, using numerical examples, we compare the <i>Gaussian</i> <i>approximation</i> to the numerical approximation of the true predictive distribution by simple Monte-Carlo. publisher: Springer date: 2005-01 type: Articles type: PeerReviewed format: text language: en identifier: https://eprints.gla.ac.uk/3719/1/GirMur05.pdf identifier: Girard, A. and Murray-Smith, R. (2005) Gaussian processes: prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series. Lecture Notes in Computer Science , 3355, pp. 158-184. (doi: 10.1007/b105497 ) relation: http://dx.doi.org/10.1007/b105497 relation: 10.1007/b105497 identifier: 10.1007/b105497