Stahel, Werner A.
Künsch, Hans R.
- Working Paper
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that solutions of stochastic advection-diffusion partial differential equations (SPDEs) provide a flexible model class for spatio-temporal processes which is computationally feasible also for large data sets. The solution of the SPDE has in general a nonseparable covariance structure. Furthermore, its parameters can be physically interpreted as explicitly modeling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. In order to obtain computationally efficient statistical algorithms we use spectral methods to solve the SPDE. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational costs of Bayesian or frequentist inference being dominated by the fast Fourier transform. The proposed model is applied to postprocessing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast to the raw forecasts from the numerical model, the postprocessed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts Show more
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Journal / seriesJournal of the Royal Statistical Society Series B, Statistical methodology
Organisational unit03217 - Künsch, Hans Rudolf
NotesSubmitted 26 March 2014, Published 27 March 2014.
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