I am reading the seminal paper

Stuart Geman and Donald Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984. doi: 10.1109/TPAMI.1984.4767596 (free pdf)

on image restoration. Is there a more recent account (paper or lecture notes) with proper generalizations and incorporating the recent progress of Bayesian methods?

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    $\begingroup$ I am not sure if this question is well posed in its current form. May be you can add some more details and "Modern account of Geman Geman 1984" seems like you have written Geman two times by mistake.. Only after opening that document it is clear that it is written by two persons with Geman in their name..Please consider editing this question.. $\endgroup$ – Praphulla Koushik Aug 30 '18 at 16:16
  • $\begingroup$ In that paper some of deep properties of Gibbs measures are used to construct a useful a priori measure. Yet, statistical mechanicss and baysian statistics have evovled a lot since 1984. Hence, the question whether a modern account is available. I know the question is vague as it is less a math question than a question about the evolution of results in statistcs and statistical mechanics. As per Geman Geman, I think people from the field will recognize the paper like this. To be sure, I added a link... $\endgroup$ – rjm Aug 30 '18 at 16:55
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    $\begingroup$ I have requested you to rewrite the question so that it is little more accessible than it is now.. It is up to you... $\endgroup$ – Praphulla Koushik Aug 30 '18 at 17:18
  • $\begingroup$ Yes I understand your point. I am after people who know the paper and the evolution of the various (statistical mechanics, Baysian inference). If no body show-up, I Ill start to decompose the question into specific theoretical aspects. I leave it broad on purpose. $\endgroup$ – rjm Aug 30 '18 at 17:24
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    $\begingroup$ See Besag, York and Mollié as a start: link.springer.com/article/10.1007/BF00116466 $\endgroup$ – David G. Stork Aug 30 '18 at 21:47

Given that the paper has accumulated a stunning 21.850 citations at Google scholar to this date and 487 are from 2018 the work is clearly influential (zbMATH lists 913 citations and 17 from 2018, MATHSCINET does not have it, though). It is not straightforward to answer your question "Is there a more recent account (paper or lecture notes) with proper generalizations and incorporating the recent progress of Bayesian methods?" since the paper contributed several things and the thousands of citations cite it for very different reasons (e.g. many references are just given for the highly useful block Gibbs sampling).

To give just one concrete pointer: You may want to have a look at

Wainwright, Martin J., and Michael I. Jordan. "Graphical models, exponential families, and variational inference." Foundations and Trends® in Machine Learning 1.1–2 (2008): 1-305.

  • $\begingroup$ Thanks a lot for your answer. It is these kind of pointers I am looking for. I agree with you as per the diversity of topics covered in this paper. And indeed, most of the Citations are about the Gibbs sampler. I am more inclined in the theoretical aspects. I will read what you suggested. $\endgroup$ – rjm Aug 31 '18 at 8:55

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