### 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 language | English |
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Pages (from-to) | 609-626 |

Number of pages | 18 |

Journal | Journal of the Royal Statistical Society: series B |

Volume | 66 |

Issue number | 3 |

DOIs | |

Publication status | Published - 13 Aug 2004 |

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### Keywords

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

### Cite this

*Journal of the Royal Statistical Society: series B*,

*66*(3), 609-626. https://doi.org/10.1111/j.1467-9868.2004.02054.x

}

*Journal of the Royal Statistical Society: series B*, vol. 66, no. 3, pp. 609-626. https://doi.org/10.1111/j.1467-9868.2004.02054.x

**Bayesian analysis of the scatterometer wind retrieval inverse problem : Some new approaches.** / Cornford, Dan; Csató, Lehel; Evans, David; Opper, Manfred.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bayesian analysis of the scatterometer wind retrieval inverse problem

T2 - Some new approaches

AU - Cornford, Dan

AU - Csató, Lehel

AU - Evans, David

AU - Opper, Manfred

PY - 2004/8/13

Y1 - 2004/8/13

N2 - 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.

AB - 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.

KW - Data assimilation

KW - Gaussian processes

KW - Markov chain monte carlo methods

KW - multimodal distributions

KW - variational methods

UR - http://www.scopus.com/inward/record.url?scp=3543032212&partnerID=8YFLogxK

UR - http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2004.02054.x/abstract

U2 - 10.1111/j.1467-9868.2004.02054.x

DO - 10.1111/j.1467-9868.2004.02054.x

M3 - Article

VL - 66

SP - 609

EP - 626

JO - Journal of the Royal Statistical Society: series B

JF - Journal of the Royal Statistical Society: series B

SN - 1369-7412

IS - 3

ER -