On the influence of the prior distribution in image reconstruction (Q2463654)

The authors propose two measures of how much a Bayesian estimate is determined by the prior distribution and to what degree it is determined by the data. The first one, the influence curve for the prior, shows how much estimates change when the prior is changed along a curve which interpolates between a flat prior, the prior in actual use, and a completely concentrated prior. Since in high-dimensional problems the influence curve may contain more information than can be digested, the authors introduce the second measure, the influence rate, which is the value of the derivative of the influence curve at the actual prior used. It is shown how the measures may be used to make simple diagnostic plots. They illustrate how the influence measures can be computed and interpreted to an image reconstruction problem from visual field testing and to a stylized image analysis problem.