Bayesian analysis of the scatterometer wind retrieval inverse problem: Some new approaches

Dan Cornford*, Lehel Csató, David Evans, Manfred Opper

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)609-626
Number of pages18
JournalJournal of the Royal Statistical Society: series B
Volume66
Issue number3
DOIs
Publication statusPublished - 13 Aug 2004

Fingerprint

Bayesian Analysis
Inverse Problem
Retrieval
Gaussian Process
Bayes
Posterior distribution
Likelihood
Nonlinear Inverse Problems
Inverse Model
Markov Chain Monte Carlo Methods
Prior distribution
Remote Sensing
Computational Complexity
Model
Observation
Bayesian analysis
Inverse problem
Approximation
Gaussian process

Keywords

  • Data assimilation
  • Gaussian processes
  • Markov chain monte carlo methods
  • multimodal distributions
  • variational methods

Cite this

Cornford, Dan ; Csató, Lehel ; Evans, David ; Opper, Manfred. / Bayesian analysis of the scatterometer wind retrieval inverse problem : Some new approaches. In: Journal of the Royal Statistical Society: series B. 2004 ; Vol. 66, No. 3. pp. 609-626.
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Bayesian analysis of the scatterometer wind retrieval inverse problem : Some new approaches. / Cornford, Dan; Csató, Lehel; Evans, David; Opper, Manfred.

In: Journal of the Royal Statistical Society: series B, Vol. 66, No. 3, 13.08.2004, p. 609-626.

Research output: Contribution to journalArticle

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