Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

On the influence of the prior distribution in image reconstruction

Rootzén, Holger LU and Olsson, Jonny LU (2006) In Computational Statistics 21(3-4). p.431-444
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
glaucoma diagnosis, visual, BAYESIAN ROBUSTNESS, SENSITIVITY, PERIMETRY, SITA, sensitivity analysis, Gibbs distribution, field test
in
Computational Statistics
volume
21
issue
3-4
pages
431 - 444
publisher
Physica Verlag
external identifiers
  • wos:000243401000004
  • scopus:33845308261
ISSN
0943-4062
DOI
10.1007/s00180-006-0004-1
language
English
LU publication?
yes
id
6818f08e-20c3-462e-9a04-37380fd42666 (old id 1417704)
date added to LUP
2016-04-01 17:10:07
date last changed
2021-02-17 06:25:15
@article{6818f08e-20c3-462e-9a04-37380fd42666,
  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.},
  author       = {Rootzén, Holger and Olsson, Jonny},
  issn         = {0943-4062},
  language     = {eng},
  number       = {3-4},
  pages        = {431--444},
  publisher    = {Physica Verlag},
  series       = {Computational Statistics},
  title        = {On the influence of the prior distribution in image reconstruction},
  url          = {http://dx.doi.org/10.1007/s00180-006-0004-1},
  doi          = {10.1007/s00180-006-0004-1},
  volume       = {21},
  year         = {2006},
}