On the influence of the prior distribution in image reconstruction

Holger Rootzén, Jonny Olsson

Research output: Contribution to journalArticlepeer-review

Abstract

Two measures of the influence of the prior distribution p(B) in Bayes estimation are proposed. Both involve comparing with alternative prior distributions proportional to p(theta)(s), for s >= 0. The first one, the influence curve for the prior distribution, is simply the curve of parameter values which are obtained as estimates when the estimation is made using p(B)s instead of p(B). It measures the overall influence of the prior. The second one, the influence rate for the prior, is the derivative of this curve at s = 1, and quantifies the sensitivity to small changes or inaccuracies in the prior distribution. We give a simple formula for the influence rate in marginal posterior mean estimation, and discuss how the influence measures may be computed and used in image processing with Markov random field priors. The results are applied to an image reconstruction problem from visual field testing and to a stylized image analysis problem.
Original languageEnglish
Pages (from-to)431-444
JournalComputational Statistics
Volume21
Issue number3-4
DOIs
Publication statusPublished - 2006

Subject classification (UKÄ)

  • Probability Theory and Statistics

Free keywords

  • glaucoma diagnosis
  • visual
  • BAYESIAN ROBUSTNESS
  • SENSITIVITY
  • PERIMETRY
  • SITA
  • sensitivity analysis
  • Gibbs distribution
  • field test

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