Bayesian spatio-temporal kriging with misspecified black-box
Résumé
We propose a new algorithm for spatio-temporal prediction. At a given time t, we use a Bayesian kriging model for spatial prediction. The temporal evolution from t to t + 1 is given by a deterministic black-box which can be a complex numerical code or a partial differential equation. As often in practice, the black-box is misspecified, in the sense that its parameters are imprecisely known or may be varying randomly over time. At time t, we use the black-box to obtain a rough prediction at time t + 1. When new data are available, the black-box is used to estimate the hyperparameters of the Bayesian kriging at time t + 1 by using Monte Carlo methods. Through a numerical application, we show that our method improves the values predicted by the black-box only.
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