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Bayesian analysis of the scatterometer wind retrieval inverse problem: some new approaches
Author(s) -
Cornford Dan,
Csató Lehel,
Evans David J.,
Opper Manfred
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2004.02054.x
Subject(s) - prior probability , markov chain monte carlo , computer science , inverse problem , bayesian inference , scatterometer , posterior probability , algorithm , gaussian process , bayesian probability , gaussian , mathematics , artificial intelligence , mathematical analysis , radar , telecommunications , physics , quantum mechanics
Summary. The retrieval of wind vectors from satellite scatterometer observations is a non‐linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.