Bayesian Analysis of the Scatterometer Wind Retrieval inverse Problem: Some new Approaches
Dan Cornford, Lehel Csato, David J Evans and Manfred Opper
Journal of the Royal Statistical Society B Volume 66, pp. 1-17, 2004.

Abstract

The retrieval of wind vectors from satellite observed radar backscatter can be seen as a non-linear inverse problem. A common approach to solving inverse problems is the Bayesian framework: to infer the posterior distribution of the latent variables of interest given the observations, a model relating the observations to the latent variables, and a prior distribution over the latent variables. In this paper we show how Gaussian process priors can be used in a variety of retrieval methods, using local forward (observation) models and direct inverse models. We present an enhanced Markov Chain Monte Carlo method to sample from the resulting multi-modal posterior distribution. We go on to show how the computational complexity of the inference can be controlled using sparse, sequential Bayesian learning for Gaussian processes. This helps to overcome the most serious barrier to the use of fully probabilistic, Gaussian processes methods in remote sensing inverse problems, where the size of the data set can become prohibitively large. We contrast the sampling results with the approximations found using the sparse sequential Gaussian process algorithm.

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