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Posterior contracti...
Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
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- Agapiou, Sergios (författare)
- The University of Warwick
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- Larsson, Stig, 1952 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics
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- Stuart, Andrew M. (författare)
- The University of Warwick
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(creator_code:org_t)
- Elsevier BV, 2013
- 2013
- Engelska.
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Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 123:10, s. 3828-3860
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Inverse problems
- Posterior consistency
- Posterior contraction
- Gaussian prior
- Posterior distribution
- Posterior consistency; Posterior contraction; Gaussian prior; Posterior distribution; Inverse problems
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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