On the influence of the prior distribution in image reconstruction
(2006) In Computational Statistics 21(34). p.431444 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:
https://lup.lub.lu.se/record/1417704
 author
 Rootzén, Holger ^{LU} and Olsson, Jonny ^{LU}
 organization
 publishing date
 2006
 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
 34
 pages
 431  444
 publisher
 Physica Verlag
 external identifiers

 wos:000243401000004
 scopus:33845308261
 ISSN
 09434062
 DOI
 10.1007/s0018000600041
 language
 English
 LU publication?
 yes
 id
 6818f08e20c3462e9a0437380fd42666 (old id 1417704)
 date added to LUP
 20160401 17:10:07
 date last changed
 20210217 06:25:15
@article{6818f08e20c3462e9a0437380fd42666, 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 = {09434062}, language = {eng}, number = {34}, pages = {431444}, publisher = {Physica Verlag}, series = {Computational Statistics}, title = {On the influence of the prior distribution in image reconstruction}, url = {http://dx.doi.org/10.1007/s0018000600041}, doi = {10.1007/s0018000600041}, volume = {21}, year = {2006}, }