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Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
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Agapiou, Sergios, Larsson, Stig and Stuart, A. M. (2013) Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems. Stochastic Processes and their Applications, Volume 123 (Number 10). pp. 3828-3860. doi:10.1016/j.spa.2013.05.001
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Official URL: http://dx.doi.org/10.1016/j.spa.2013.05.001
Abstract
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||
| Publisher: | Elsevier Science BV | ||||
| ISSN: | 0304-4149 | ||||
| Official Date: | October 2013 | ||||
| Dates: |
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| Volume: | Volume 123 | ||||
| Number: | Number 10 | ||||
| Page Range: | pp. 3828-3860 | ||||
| DOI: | 10.1016/j.spa.2013.05.001 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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