Bayesian inference for wind field retrieval

In many problems in spatial statistics it is necessary to infer a global problem solution by combining local models. A principled approach to this problem is to develop a global probabilistic model for the relationships between local variables and to use this as the prior in a Bayesian inference procedure. We use a Gaussian process with hyper-parameters estimated from numerical weather prediction models, which yields meteorologically convincing wind fields. We use neural networks to make local estimates of wind vector probabilities. The resulting inference problem cannot be solved analytically, but Markov Chain Monte Carlo methods allow us to retrieve accurate wind fields.