#67. Old paper by Colubi et al.

A survey on fuzzy random variables from the point of view of Statistics.

Ana Colubi, Renato Coppi, Pierpaolo D'Urso, María Ángeles Gil (2007). Statistics with fuzzy random variables. Metron 65, 277-303.

It gives a good overview of what the Oviedo group has been doing for many years now, anyway I feel the survey is maybe too self-centered to be fair to other researchers.

#66. Old paper by Shafer and Vovk

I presume you have heard about Glenn Shafer and Vladimir Vovk's game-theoretic approach to probability, so this one travels a different (but not really disjoint) path.

In this paper they trace the early history of measure-theoretical probability culminating in Kolmogorov's well-known book.

Glenn Shafer, Vladimir Vovk (2006). The sources of Kolmogorov’s Grundbegriffe. Statistical Science 21, 70--98.

Their account is nice and very informative, not avoiding technical details. It's a pity people don't pay historical issues more attention.

#65. Old papers by Volker Krätschmer

You can find Krätschmer's papers here at his website.

After working for some years on fuzzy random variables and related problems, Volker, like a number of other capable researchers, recently moved on to greener pastures (probability in finance).

Specially interesting are his four papers published in 2006.

In his Test paper he discusses at length several extensions of known vector-valued integrals (Bochner and Pettis) to fuzzy random variables. The other three papers, two of them in the Journal of Multivariate Analysis, are one least squares estimation with fuzzy random variables, including "sqrt n" consistency and limit distributions, which I have never seen discussed elsewhere.

#64. Forthcoming book by Reinhard Viertl

A number of online sellers are already accepting preorders of Reinhard Viertl's new book Fuzzy data and Statistics, seemingly to appear in Dec 2009 in Wiley.

As the name `Wiley' may suggest, this will be the third time (to the best of my knowledge) that fuzzy material makes it into the Wiley Series on Probability and Statistics.

First, Finding groups in data: an introduction to cluster analysis (1990, by Kaufman and Rousseeuw) discussed fuzzy and nonfuzzy clustering on equal footing.

Second came Statistical applications using fuzzy sets (1994, by Manton, Woodbury and Tolley), whose grade-of-membership method made heavy use of fuzzy partitions (although, it looks like currently the fuzzy interpretation has been expurgated from the theory).

#63. Old paper by Coppi, Gil and Kiers

This paper introduced the CSDA special issue on The fuzzy approach to Statistics. Before presenting the papers in that issue, it presents Coppi's self-called `informational paradigm' which inserts Statistics in a wider landscape of information management and knowledge acquisition tasks.

Renato Coppi, María Ángeles Gil, Henk A. L. Kiers (2006). The fuzzy approach to statistical analysis. Computational Statistics and Data Analysis 51, 1-14.


Here you are another document, now found at the Italian Statistical Association website, in case it is clarifying:

Renato Coppi (2007?). The treatment of different sources of uncertainty affecting the data and the statistical models according to the Informational Paradigm.

#62. Old paper by Laviolette and Seaman

Luckily, I've found another paper I have wanted to link to since I started this blog.

I have very little good to say about it and I believe it did do a serious disservice to its cause. Anyway, it has considerable historical interest.


Michael Laviolette, John W. Seaman Jr. (1994). The efficacy of fuzzy representations of uncertainty. IEEE Transactions on Fuzzy Systems 2, 4-15.

This paper was discussed in pages 16-42 as you can see here.

#61. Old papers on fuzzy set elicitation

There are plenty of papers on how to elicit fuzzy sets. These have a strong emphasis on measurement-theoretical aspects.

Feel free to suggest in the comments more interesting papers like these (or with a different emphasis).

Jay Verkuilen (2005). Assigning membership in a fuzzy set analysis. Sociological Methods and Research 33, 462--496.

(A recent survey with a social science twist.)

Taner Bilgiç, Burhan Turksen (1999). Measurement Of membership functions: theoretical and empirical work. Chapter 3 in Fundamentals of Fuzzy Sets (Didier Dubois, Henri Prade, editors), 195-230.

(I presume everybody knows this one, an excellent starting point.)

#60. Old paper by Witold Pedrycz

I presume a thorough search would discover many interesting papers by Pedrycz in the net. This one makes a nice reading:

Witold Pedrycz (2007). Collaborative and knowledge-based fuzzy clustering. International Journal of Innovative
Computing, Information and Control 3, 1-12.

The content is much more `philosophical' than `technical', explaining some ideas from his `human-centric' view of clustering techniques. I recall distinctly Pedrycz's talk from IFSA'05 (Dubois's as well, but that's material for another post). A catchy example of Pedrycz's was a system which would learn to classify your digital picture collection. I thought: Now that's definitely a clustering problem and how far it is from the typical view of clustering in statistical books and journals!


More technical material can be found in Pedrycz's book (link to Google Books).

Witold Pedrycz (2005). Knowledge-based clustering: from data to information granules. Wiley, Hoboken.

#59. Old paper by Lotfi Zadeh

Related to the Singpurwalla-Booker paper just below is, of course, Zadeh's original paper on probability of fuzzy events.

Lotfi A. Zadeh (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421-427.


More papers by Zadeh can be found here.


A nice Powerpoint presentation based on (the short version of) Dubois and Prade's Fuzzy sets and probability: Misunderstandings, bridges and gaps, where fuzzy events play a role, can be found here.


If that weren't enough, Gert de Cooman recently discussed the issue here in his blog.

#58. Old paper by Singpurwalla and Booker

I have often googled to find a free copy of this paper since I started this blog.

Nozer Singpurwalla, Jane A. Booker (2004). Membership functions and probability measures of fuzzy sets. Journal of the American Statistical Association 99, 867-877.

Here is my review of it for Mathematical Reviews.

As I say there, I believe that it will be remembered as the first attempt to transmute fuzzy sets into something palatable to hardcore Bayesians.

#57. Old chapter by Thoralf Skolem

Via Project Euclid, one can access Skolem's Abstract set theory (70-page lecture notes published by the University of Notre Dame). Its Chapter 18 summarizes very briefly Skolem's approach to proving the consistency of set theory within Lukasiewicz [0,1]-valued logic.

Just a curiosity, but--

Thoralf Skolem (1962). The possibility of set theory based on many-valued logic.

The whole volume can be downloaded chapter by chapter here.

#56. Old paper by Glen Meeden

Meeden co-authored the paper on fuzzy p-values which sadly seems to have made little or no impact in the fuzzy statistics community.

In this recent paper, he discusses his views on probability-possibility `translation'. In spite of the title, I say so because I think he means a possibility distribution when he says 'a fuzzy set'.

Meeden seems to be unaware of the literature in this topic, but anyway his approach has a rather Bayesian flavour by making it a loss-driven decision, and that's nice (although, a criticism in point is that his loss functions lack a fuzzy interpretation).

Glen Meeden (2008). Fuzzy set representation of a prior distribution. In: Pushing the limits of contemporary Statistics: Contributions in honor of Jayanta K. Ghosh, 82-88. Published by the IMS.


One further fuzzy preprint is:

Glen Meeden, Siamak Noorbaloochi. Hypotheses testing as a fuzzy set estimation problem. Available as a technical report from the University of Minnesota.


More papers of his can be found here.

#55. Old book by Nguyen and Wu

As it turns out, someone has uploaded Hung Nguyen and Berlin Wu's Fundamentals of statistics with fuzzy data (Springer, 2006) to direct download servers. I didn't put it there and I ignore who did it, in particular if he had the legal right to do so. If you are uncomfortable with that, or think that downloading the book may be illegal in your country, just use Google Books or inter-library loan instead.


Instructions: In this page, follow the "Rapidshare" link (if it doesn't work, try the "File Factory" link but the process is then more complex), then click on the button "Free user", wait for as long as you're asked to do, finally a button "Download" will appear, click on it. The PDF is compressed as a RAR file, so you will need a decompressor for it. If you haven't any, google for e.g. WinRAR and download a shareware version for free.

#54. Special issue on Fuzzy Sets and Statistics (CFP)

Computational Statistics and Data Analysis is preparing their second special issue on Fuzzy Sets and Statistics, this time with Ana Colubi, Didier Dubois and Frank Klawonn serving as guest editors.

The deadline is December 15th, 2009. However you may also be interested in submitting a conference version of the paper to the track Fuzzy Statistical Analysis of the 2nd International Workshop of the ERCIM Working Group on Computing & Statistics, in which case a prior deadline for 1-page abstracts is June 1st, 2009.

Update: July 31st, 2009.

Further info here and here, respectively.

#53. Essay at edge.org

This is an interesting essay I found while surfing the net.

Nassim Nicholas Taleb (2008). The fourth quadrant. A map of the limits of statistics.

The main point is that mind habits (got by osmosis or lack of deep understanding) obtained in ordinary statistics courses are dangerous in decision-making with extreme value distributions. The text leans towards the role of extreme events in wrong risk assessment leading to the current economic crisis.

Although the point of view is strictly probabilistic, there is a resonance with some important ideas behind `alternative' uncertainty modelling. For instance,

"Are we using models of uncertainty to produce certainties?"

"Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations—each would extrapolate differently outside the set of events on which it was derived."


---
If you find the essay interesting: in the last SMPS, Dominique Guyonnet gave a keynote lecture on possibilistic risk analysis for enviromental decisions which is very nice to follow. The paper is in the conference proceedings.

#52. New special issue of FSS

Issue 160(3) of Fuzzy Sets and Systems (February 2009), guest edited by Erich Peter Klement and Radko Mesiar, is a special issue with selected papers from Linz 2007. The topic is Fuzzy sets, probabilities, and statistics: gaps and bridges.

The table of contents is as follows.

Editorial
Page 291
Erich Peter Klement, Radko Mesiar

Fuzzy inclusion and similarity through coherent conditional probability
Pages 292-305
Romano Scozzafava, Barbara Vantaggi

T-conditional possibilities: Coherence and inference
Pages 306-324
Giulianella Coletti, Barbara Vantaggi

A concept of duality for multivariate exchangeable survival models
Pages 325-333
Fabio Spizzichino

On a class of transformations of copulas and quasi-copulas
Pages 334-343
Elisabetta Alvoni, Pier Luigi Papini, Fabio Spizzichino

Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data
Pages 344-356
Ana Colubi

Estimation of a simple linear regression model for fuzzy random variables
Pages 357-370
Gil González-Rodríguez, Ángela Blanco, Ana Colubi, M. Asunción Lubiano

Uncertainty measures—Problems concerning additivity
Pages 371-383
Siegfried Weber


The issue also contains the following regular paper, which anyway is on-topic so I include it here as well.

A Monte Carlo-based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type
Pages 384-401
Diego A. Alvarez


---
The proceedings of the seminar can be found here.

#51. Old paper by Dubois and Hüllermeier

No time lately.


Didier Dubois, Eyke Hüllermeier (2007). Comparing probability measures using possibility theory: A notion of relative peakedness. Int. J. Approx. Reasoning 45, 364-385.

#50. Off-topic

For the interested readers, you can download the mamooth paper of Anton Kapustin and Edward Witten, 231 pages widely known as the Kapustin-Witten paper, from the net.

Electric-magnetic duality and the geometric Langlands program (2006).

That was written in 2006 and, as far as I know, is still unpublished or was never meant to be published traditionally.

You can also download the more recent lectures notes of Kapustin on the same topic, based on a 2007 course. They amount to a mere 38 pages and may be more readable.

Lectures on electric-magnetic duality and the geometric Langlands program


And no, I don't understand a word of what these gentlemen say but I will make my way through it anyway.

49. Editorial post

We are about to reach fifty posts and one year and a half on the net.

When I started this blog, I thought I'd send an e-mail informing each cited researcher. However, I felt that if only few posts were available, they would classify the blog as an anecdote of little use and probably not be back. So I sent the blog's address only to close friends and colleagues.

Now, the blog has received 1,349 visits and ranks in fifth position (over 280,000 search results) when you google for "fuzzy sets"+"statistics". One thousand visits is a modest number for a common blog (my personal blog has had 19,000 page loads in the same time, and it's a modest one) but maybe not so when the information delivered is so highly specialized and arrives at a slow rate of two posts per month.

The blog looks quite serious now and contains many links to interesting papers and books. As an important development, I have added a box in the right column so that readers can have the new posts delivered at their e-mail address. So I think it's about time to undertake the task of promoting the SPFS blog by informing all cited researchers that their work has been linked here.


As to `editorial' decisions to be announced at a moment like this, there are three of those.

1. Post 25 was off-topic and I have decided that a 4% of off-topic posts is OK.

2. Begining with post 51, a number of entries will be devoted to linking to the SPFS material in Google Books. If you know, Google has been digitalizing books for some time, with or without permission from copyright owners, and I've been shocked to find out how much material is there. It will take some time to make a careful search and organize the results, though.

3. Some effort in the following direction will be made: posting about applications and presence of fuzzy statistical methods in different fields. For instance, I have long wanted to write a post about fuzzy methods for microarray data (I downloaded a couple of papers but were not very good).


And, finally, an observation. If you remember, only links to publicly accessible papers are posted, so it's a little frustrating to me when I find good new papers that can be accessed only on a pay-a-third-party basis. I bring to everybody's attention that currently many publishers will let you retain the right to post your papers at your website, or at a public repository. You needn't go through creating and maintaining a website to have them accessible to everyone: a blog and a file hosting service is all you need, and there are plenty of free providers for both things. Actually, you can get started in less than ten minutes.

48. New paper by Arnold Shapiro

An introduction to fuzzy random variables, intended for an actuarial science audience.

Arnold F. Shapiro. A fuzzy random variable primer.

It may be worth pointing out that Shapiro was awarded the second-best-presentation award in the 42nd Actuarial Research Conference (August 2007) for this paper.

47. Old book by Edwin Jaynes

I thought the `preprint' version of Jaynes's book had been removed from the Internet when it was published in paper. Either I was wrong, or it is back there anyway. It can be downloaded, chapter by chapter (30 chapters plus 9 appendices), as PS files. Be aware that these files are not final (or they weren't the first time I found them) as Jaynes died before finishing the book, leaving some parts unfinished, and the final version was prepared by Larry Bretthorst.

Edwin T. Jaynes (2003). Probability Theory. The logic of science. Cambdridge Univ. Press, Cambridge.

Sometimes lucid, sometimes irritating, sometimes enlightening, often misguiding.

46. Old theses by Körner, Hébert and myself

I finally found Ralf Körner's thesis

Ralf Körner (1997). Linear models with random fuzzy variables

at his old website at Freiberg. Some preprints can be found there too.

Moreover, I've found P.-A. Hébert's

Pierre-Alexandre Hébert (2004). Analyse de données sensorielles : une approche ordinale floue (Sensorial data analysis: an ordinal fuzzy approach).

It seems fair enough to add my own thesis here, even if it were only to make this really multi-language.

Pedro Terán (2003). Teoremas de aproximación y convergencia para conjuntos y funciones aleatorias (Approximation and convergence theorems for random sets and random functions).

45. Old papers by Thierry Denœux and co-workers

Denœux works, among other things, on fuzzy data analysis. He is one of several people who have started devising methods for fitting fuzzy measures to empirical data.

Some papers of his can be found here at his website.

44. Old paper by Baudrit, Couso and Dubois

Hybrid methods for uncertainty modelling are in their infancy. I suspect we might be missing a whole layer of deeper concepts underlying the familiar notions of probability, possibility, etcetera.

The near future, hierarchical Bayesian modelling rising exponentially, may be dark for some time for realistic approaches. Ideally, we'd need a compelling foundation* which would suggest simple practical implementations, reasonable for practitioners.

Cédric Baudrit, Inés Couso, Didier Dubois (2007). Joint propagation of probability and possibility in risk analysis: towards a formal framework. Int. J. Approx. Reasoning 45, 82-105.


* No, I don't find Bayesian foundations compelling at all.

43. SMPS'08: Deadline extended

The deadline for paper submission to the 4th International Conference on Soft Methods in Probability and Statistics has moved from Feb 1st to Feb 11th.

42. Advice on starting to get published in Statistics and Probability journals

Unfortunately, there is little mutual interest or communication between typical fuzzy researchers and typical statistics researchers.

There seem to be two positions among SPFS researchers. Some of them think it's fine to have all their papers published in, say, FSS or INS or IEEE:TFS. That, I acknowledge, is good for their position within the fuzzy community, since many people just don't check non-fuzzy journals and so the efficacy of their efforts to get visible is undivided. Others think that publications should be allocated among fuzzy and non-fuzzy journals alike.

In order to do the latter, one needs to know which Statistics journals are better than others, and which give fuzzy papers a fair chance.

My advice is: you will lose less time if you don't bother to submit to journals which haven't published fuzzy papers for some time. On the other hand, some statistical journals have sustainedly published fuzzy material or don't have bizarre objections to it, for instance (in no particular order; more names will be added as they come to my mind)

Computational Statistics and Data Analysis
Metrika
Statistics and Probability Letters
Test

Publishing fuzzy in JCR-covered Probability journals is extremely hard, and although winning the lottery may need more luck, I'm not sure. They are very few, of good quality and they prefer their own fashionable topics. An exception is Stochastic Analysis and Applications, which has published some fuzzy material of a very specific nature.

Thus you would do better, paradoxically, in general math journals. A couple of journals I've had a very pleasant experience publishing with are

Journal of Approximation Theory
Proceedings of the American Mathematical Society

I recommend that you avoid the Journal of Mathematical Analysis and Applications. Not only it will avoid you anyway if you don't, but it's by large the less serious journal I've ever submitted to.

As far as journal quality or prestige is concerned, if you look at the journals' editorial boards without recognizing any name on it, you may want to trust me on the following recommendation.

First, download this document. It contains the tables in the following paper:

V.Theoharakis, M.Skordia (2003). How Do Statisticians Perceive Statistics Journals? American Statistician 57, 115-123.

You may also get the paper, but the tables contain all the information. As you will see, they are very informative.

Second, if you wish to use an objective ranking, my advice is that you may like the Article Influence indicator calculated by eigenfactor.org rather than the well-known company-owned Impact Factor. The AI can be accessed free and is calculated from the same data. It uses the Page Rank algorithm developed by Google to rank websites.

I know of three such rankings:
-The Impact Factor introduces some serious distortions in the ranking.
-The brand new SCImago ranking (which uses the SCOPUS database) is seriously wrong. However the SCImago website will provide you with an SCOPUS-based Impact Factor which you can access for free, and also a sort of Hirsch index for the journals.
-The Article Influence gives the least bad ranking, in fact it's quite good, but it fails for journals with few papers a year, so only about 50 journals are listed, as opposed to about 90 for the other two.

---
Readers' comments and further advice for beginners are welcome.

41. Old tutorial by José Miguel Bernardo

You may take Bayesianism as a methodology or as a religion (you know, the "...the very guide of life" thing). Both aspects are blended. Everything that makes it fascinating as a methodology is also evidence that, as a religion, it qualifies at the crackpot level.

More precisely, if you accept a number of axioms, then you can solve every problem, and the way to solve them is the same, universally. Bayesianism provides a full theory of uncertainty working under a number of specified assumptions. Of course, it is very difficult (to me) to imagine how those assumptions could be met except in a tiny minority of the problems involving uncertainty.

Some people have a much more powerful imagination than mine, but except for that important excess and its consequences they are a joy to read.

J.M. Bernardo. Bayesian Statistics.

This is a fast-paced introduction to Bayesian Statistics, including a lot of the somewhat deeper technical material, often absent from introductions, which unbelievers should at least know and understand.

His style, though, is at times an unpleasant and dogmatic one.

More papers by José Miguel Bernardo, including several published revamps (some earlier, some later) of this document, can be found here at his website. Don't miss the Test paper on intrinsic regions.

40. Old survey papers by Grzegorzewski and Hryniewicz, and Taheri

I bring you two papers surveying different aspects of fuzzy statistics. Unfortunately, they are no longer representative of what's currently being done, and I'd rather call this `old Fuzzy Statistics' (but that's another story). In any case, they can be a good source for old references.

Przemyslaw Grzegorzewski, Olgierd Hryniewicz (1997). Testing statistical hypotheses in a fuzzy environment. Mathware & Soft Computing 4, 203-217.

S. Mahmoud Taheri (2003). Trends in Fuzzy Statistics. Austrian Journal of Statistics 32, 239-257.

It must be noted that the second paper covers favorite topics developed within the `fuzzy+statistics' community but makes no attempt at discussing the non-fuzzy literature, thus ignoring important topics like fuzzy clustering, to name just an instance.

39. Old paper by Matteo Paris

A curious paper which uses fuzzy hypothesis testing.

Matteo G. A. Paris (2001). Nearly ideal binary communication in squeezed channels. Physical Review A 64, paper 014304, 1-4.

38. New paper by Kulinskaya and Lewin

Fuzzy p-values continue to attract researchers (see more papers here).

On fuzzy FWER and FDR procedures for discrete distributions by Elena Kulinskaya and Alex Lewin.

37. New theme-oriented issue of FSS

Volume 159 issue 3 of Fuzzy Sets and Systems (February 2008) is devoted to the theme Probability and Statistics. This is not a guest-edited special issue but an ordinary issue where all papers are on the same topic.

FSS has been doing this for a while; it is more practical as it makes harder to miss a paper on your topic, but at the same time it implicitly acknowledges that `fuzzy' has become too broad to be much of a unitarily focused discipline.

The table of contents is as follows.

·Probability and fuzzy sets

1. Higher order models for fuzzy random variables
Pages 237-258
Inés Couso and Luciano Sánchez

2. A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability
Pages 259-269
W. Trutschnig

·Random sets

3. Approximation techniques for the transformation of fuzzy sets into random sets
Pages 270-288
Mihai Cristian Florea, Anne-Laure Jousselme, Dominic Grenier and Éloi Bossé

4. Nonspecificity for infinite random sets of indexable type
Pages 289-306
Diego A. Alvarez

·Applications

5. Fuzzy universal generating functions for multi-state system reliability assessment
Pages 307-324
Yi Ding and Anatoly Lisnianski

6. Optimal selection of the service rate for a finite input source fuzzy queuing system
Pages 325-342
María José Pardo and David de la Fuente

·Mathematical aspects

7. Strong law of large numbers for t-normed arithmetics
Pages 343-360
Pedro Terán

8. Statistical convergence in fuzzy normed linear spaces
Pages 361-370
C. Şençı˙men and S. Pehlı˙van


(Curiously, nothing less than three papers by people from, or educated in, the University of Oviedo!)

36. Old papers in AoMS (I)

This is the first in a series of entries on highly cited papers originally published in the Annals of Mathematical Statistics (1930-1972), now available at Project Euclid. I got the citation info from the ISI database.

These papers need not have any relationship, direct or whatsoever, with fuzzy sets-- but don't let that bother you.

Let us begin with the ten highest cited papers from that journal.

1. (2249 citations) Mann and Whitney on the Mann-Whitney-Wilcoxon test.
2. (1430 citations) Parzen on density estimation.
3. (1047 citations) Kullback and Leibler on Kullback-Leibler divergence.
4. (904 citations) Huber on robust estimation.
5. (815 citations) Box and Muller on the Box-Muller transform.
6. (811 citations) Robbins and Monro on the Robbins-Monro stochastic approximation method.
7. (783 citations) Chernoff on asymptotic efficiency (including the germ of the Chernoff bound, see Theorem 1).
8. (699 citations) Levene on `a matching problem arising in Genetics'.
9. (677 citations) Dempster on upper and lower probabilities (later to become a part of Dempster-Shafer theory).
10. (629 citations) Geisser and Greenhouse on the Geisser-Greenhouse correction.

This list strongly suggests that it was naive on Parzen and Huber's part to propose the names `kernel' and `M-estimator'. Don't name things too hastily!

35. Copula wiki website

It looks like there's a wiki for everything, copulas included.

34. New paper by McNeil and Nešlehová

A paper on Archimedean copulas with some new ideas, maybe worth scanning for people working on t-norms.

Alexander J. McNeil, Johanna Nešlehová. Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions. Annals of Statistics, to appear.

33. Book chapter by Jon Williamson

Although Williamson is not the kind of philosopher I would trust to guide me through a minefield (and what else is a philosopher's duty?), the following is interesting as an introduction to the various interpretations of probability.

J. Williamson (2006). Philosophies of probability: objective Bayesianism and its challenges, in Andrew Irvine (ed.): Handbook of the Philosophy of Mathematics, Volume 4 of the Handbook of the Philosophy of Science, Elsevier.

The reference comes from Williamson's website, yet it may well be wrong in the light of this.

Note also that Williamson's usage of the term `objective Bayesianism' differs from the common one in Statistics. Thus his prototype of an objective Bayesian is Jaynes, not Bernardo. It is unclear whether Williamson would call Bernardo a Bayesian at all.

More papers by Jon Williamson can be found here.

32. Old papers by Gordaliza, Matrán et al.

I have run this blog for a year without remembering AoS had published these two papers where probability of fuzzy events plays a role. OK, here you are now.

J.A. Cuesta-Albertos, A. Gordaliza, C. Matrán (1997). Trimmed k-means: an attempt to robustify quantizers, Annals of Statistics 25, 553-576.

L.A. García-Escudero, A. Gordaliza, C. Matrán (1999). A central limit theorem for multivariate generalized trimmed k-means. Annals of Statistics 27, 1061-1079.

Let me quote from the first paper: Notice that the functions ... are a natural generalization of the indicator functions of sets which have probability α (resp. at least α) obtained by introducing the possibility of partial participation of the points in the trimmings.

31. Old papers in Statistical Science

In its early days (2, 1-44, 1987), Statistical Science published a `multi-discussion' on uncertainty modelling in Artificial Intelligence. Old journal material is now freely available and you can access the papers here at Project Euclid.

The contents are as follows:

In This Issue
1-2 [contains interesting background info]

Probability Judgment in Artificial Intelligence and Expert Systems
Glenn Shafer; 3-16

The Probability Approach to the Treatment of Uncertainty in Artificial Intelligence and Expert Systems
Dennis V. Lindley; 17-24

Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty
David J. Spiegelhalter; 25-30

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
Stephen R. Watson; 30-32

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
A. P. Dempster and Augustine Kong; 32-36

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
Glenn Shafer; 37-38

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment: A Tale of Two Wells
Dennis V. Lindley; 38-40

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
David J. Spiegelhalter; 40-41

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
Glenn Shafer; 41-42

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
Dennis V. Lindley; 42-43

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
David J. Spiegelhalter; 43-44

30. SMPS'08 CFP

As you may know, the 4th International Conference on Soft Methods in Statistics and Probability will be in Toulouse (France), September 2008.

Here you are the call for papers. The submission deadline is February 1st.

29. Old paper by Genest and Favre

Copulas are currently a very important interface between Fuzzy Sets and Statistics. They used to be quite obscure and exotic to the average statistician (conditional on his ever having heard about them), but recent years are witnessing a sudden eclosion of interest and systematic application to dependence modelling, specially in areas like Finance.

The following is an interesting introduction to the statistical side of the subject.

C. Genest, A.-C. Favre (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 12, 347-368.

A full list of Christian Genest's recent publications, with many links, is here.

28. Scholarpedia entries

I've just found out that there is something called Scholarpedia which is essentially an elitist version of the popular Wikipedia. I'm no big fan of this idea, even if scientific articles in the Wikipedia may contain serious errors. In any case, it must be admitted that many choices of authors are simply right (e.g. Berger for `Bayesian Statistics' or Dubois-Prade for `Possibility Theory').

Here you are a list of on-topic articles (actually, only a small number of articles have been written so far).

Fuzzy C-Means Cluster Analysis (James C. Bezdek)
Fuzzy logic (Lotfi A. Zadeh)
Fuzzy sets (Milan Mares)
Possibility Theory (Didier Dubois, Henri Prade)
Random sets (Hung T. Nguyen)

27b. New paper by Mark Colyvan

Yet Lindley must not have made such a convincing case when, two decades later, papers like the following continue to be published.

M.Colyvan. Is probability the only coherent approach to uncertainty?, Risk Analysis, to appear.

Colyvan examines the Cox theorem from the logical point of view, more deeply than he did in an IJAR paper some years ago. Unfortunately, it is obvious from reading Lindley's testament Understanding uncertainty (Wiley, 2006) that Lindley never came to understand or accept that discussing the underlying logical assumptions is very pertinent and necessary here.

That explains that Lindley speaks of the "self-evidentiary nature" of "rules whose violation would look ridiculous" and are "dictated to us by the inexorable rules of logic" (here, p.19), whereas Colyvan puts it as follows: "Anyone wishing to argue against fuzzy methods, for instance, must not simply beg the question against those methods. To use a theorem such as Cox's theorem that is based on assumptions that fuzzy logic rejects is thus unappropriate unless the assumptions in question can be independently defended. But then the appeal to Cox's theorem is redundant" (p.11).

It is quite transparent, from the very first page of Understanding uncertainty, that Lindley lives in a world where events either happen or not happen. Thence, invoking the "inexorable rules of logic" his opponents do deny is just question-begging.

27a. Old paper by Dennis Lindley

Lindley's famous paper (mostly on the basis of Zadeh's systematic citation campaign) is available online:

D.V.Lindley (1987). The probability approach to the treatment of uncertainty in Artificial Intelligence and Expert Systems. Statistical Science 2, 3--44.

This is where the well-known paragraph "The only satisfactory description of uncertainty is probability. By this is meant that every uncertainty statement must be in the form of a probability; that several uncertainties must be combined using the rules of probability; and that the calculus of probabilities is adequate to handle all situations involving uncertainty" comes from.

26. Old chapter by Ross, Booker and Parkinson

A quite interesting sample chapter from the book Fuzzy logic and probability applications: bridging the gap (SIAM, 2002), edited by Timothy J. Ross, Jane M. Booker and W. Jerry Parkinson is freely available.

Chapter 1: Introduction, authored by the editors.

25. Off-topic

Every rule calls for an exception, or so they say.

For the interested readers, you can download the book Noncommutative Geometry, Quantum Fields and Motives by Alain Connes and Matilde Marcolli (645-page, july 2007 version) here.

Update: the book has been published by the American Mathematical Society.

24. Old paper by Tversky and Kahneman

Another interesting old paper found while looking for something else:

A. Tverski, D. Kahneman (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90, 293-315.

23. Old theses at the Université de Savoie

You can find here a list of the theses presented at the LISTIC laboratory of the Université de Savoie, including the following (in French).

Virginie Lasserre (1999). Modélisation floue des incertitudes de mesures de capteurs (Fuzzy modelling of measurement uncertainties in sensors).

Lotfi Khodja (1997). Contribution à la classification floue non supervisée (A contribution to unsupervised fuzzy classification).

22. Linz 2007 abstract book

The abstract book from the 28th Linz Seminar, entitled Fuzzy Sets, Probability and Statistics - Gaps and bridges, can be downloaded here.

21. SMPS'08

Early news about the 4th International Conference on Soft Methods in Probability and Statistics are as follows:

Spatio-temporal coordinates: Toulouse (France), September 8-10, 2008.

Submission deadline: February 1, 2008.

20. Special issue on Imprecision (CFP)

The Journal of Statistical Theory and Practice is calling for papers for its special issue on Imprecision. Guest editors are Thomas Augustin, Frank Coolen, Pauline Coolen-Schrijner and Matthias Troffaes. The deadline for submission is October 31, 2007.

Please find all the information here. Also find a valuable bibliography list on the topic here.

19. Old papers by Gert de Cooman

Preprint versions of De Cooman's papers on imprecise probabilities are here.

I'll update this entry to provide direct links to some of them.

18. Old papers by Yuhu Feng

Feng's papers on fuzzy random variables are online here.

The link points to file 26.pdf; just go backwards to 1.pdf to find the others. The papers are not ordered cronologically. A few links are broken.

I feel obliged to comment that some of Feng's papers contain wrong proofs or/and results.

17. Uncertainty in Engineering website

Here is a link to the website Uncertainty in Engineering, with material mostly based on the book Fuzzy randomness by Bernd Möller and Michael Beer. The site is kept by the same Dresden research group.

16. Andrzej Pownuk's fuzzy-probability website

Andrzej Pownuk's website with many links (up to 2004) to papers, Usenet discussions, etc. on fuzzy sets and probability.

15. New papers on fuzzy p-values

As you may know, the notion of a fuzzy p-value in the sense of Geyer and Meeden has been warmly received by the statistical community (taking into account the cyclic FS-bashing episodes over decades, 'warmly' is a good thing).

Here you are some papers:

Fuzzy p-values in latent variable problems by Elizabeth Thompson and Charles Geyer. Update: Biometrika 94 (2007), 49-60.

Fuzzy p-values and ties in nonparametric tests by Charles Geyer.

Uncertainty in inheritance: assessing evidence for linkage by Elizabeth Thompson.

Interpreting significance in nonparametric linkage analysis: the fuzzy p-value distribution extended to multiple score functions by Lars Ängquist.

14. Old paper in Test

The Spanish Statistics & OR Society (SEIO) has discontinued the website of their journal Test, which will now be editorially handled by Springer. It looks like, as a more or less tragic (and difficult to explain) consequence, papers published in the last years or forthcoming will no longer be freely accessible.

Here you are a link to the SPFS paper I've been able to rescue using Google. The link will eventually be discontinued as well: Integrals of random fuzzy sets by Volker Krätschmer.

This paper appeared in Test 15 (2006). It contains an extensive study of integrals of fuzzy random variables with convex values, defined via embeddings into Lp spaces.

Update: The SEIO website will temporarily keep accessible Test papers published in 2005 and 2006.

13. Old paper by Masson and Denœux

Another paper from Citeseer.

It is important that attention be paid to adapting modern statistical techniques to fuzzy data. Multidimensional scaling of fuzzy dissimilarity data does so for this technique which aims at visually helpful lower-dimensional representations of dissimilarities between objects. The nutshell idea is that similar objects are plotted as points at close distance, while dissimilar ones are farther apart. In this paper, dissimilarities are modelled by fuzzy numbers, whence objects are represented by fuzzy sets which appear in the plot as nice shadowed areas.

This paper appeared in Fuzzy Sets and Systems 128 (2002), 339-352.

12. Old papers by Körner and Näther

Some years ago I downloaded Ralf Körner's Ph.D. thesis from somewhere in the net but, unfortunately, it seems to have disappeared.

Anyway I have found at Citeseer a couple of papers thereof:

On the variance of fuzzy random variables. This paper by Körner appeared in Fuzzy Sets and Systems 92 (1997), 83-93.

May I bring to your attention that a definition of variance in the non-convex case is lacking.

Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates. This paper by Körner and Näther appeared in Information Sciences 109 (1998), 95-118.

11. Two papers in a forthcoming special issue of FSS

The forthcoming special issue of Fuzzy Sets and Systems on Fundamentals of fuzzy logic and soft computing and some applications, edited by Yingming Liu, Mingsheng Ying and Guoqing Chen, will contain seven selected papers from the 11th World Congress of IFSA (Beijing, 2005).

Two of those papers are relevant to this blog:

Representation theorems, set-valued and fuzzy set-valued Ito integral
Shoumei Li and Aihong Ren

Probabilistic foundations for measurement modelling with fuzzy random variables
Pedro Terán

I'll try to talk Shoumei and Aihong into uploading theirs.

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Open-minded readers are urged not to miss Ulrich Höhle's two-part paper on the relationship between fuzzy set theory and sheaf theory, to appear in FSS. Update: FSS 158 (11), 1143-1174 and 1175-1212.

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Readers are reminded that I gladly accept link submissions.

10. Old paper by Gustave Choquet

Happy and prosperous new year!

I've found out that Choquet's mammooth paper is available for free at the French server Numdam: Theory of capacities.

This paper appeared in Annales de l'institut Fourier 5 (1954), 131-295. It is one of those papers divided in chapters, so I will not try to summarize its content.

It suffices to say that it contains a handful of notions and theorems which now carry Choquet's name, including the Choquet integral and the Choquet Theorem which is essential in the theory of random sets (both of which are of minor importance in the overall context of the paper -this gives you an idea of the magnitude of this work).

9. New special issue of CSDA

The special issue of Computational Statistics and Data Analysis on The fuzzy approach to Statistics is no longer "forthcoming".

Volume 51, issue 1 of CSDA contains nothing less than 25 papers. Some of them present overviews of specific aspects of the SPFS interface.

The table of contents is as follows:

The fuzzy approach to statistical analysis
Pages 1-14
Renato Coppi, Maria A. Gil and Henk A.L. Kiers

Generalized theory of uncertainty (GTU)—principal concepts and ideas
Pages 15-46
Lotfi A. Zadeh

Possibility theory and statistical reasoning
Pages 47-69
Didier Dubois

Random and fuzzy sets in coarse data analysis
Pages 70-85
Hung T. Nguyen and Berlin Wu

Practical representations of incomplete probabilistic knowledge
Pages 86-108
C. Baudrit and D. Dubois

Tools for fuzzy random variables: Embeddings and measurabilities
Pages 109-114
Miguel López-Díaz and Dan A. Ralescu

Conditional probability and fuzzy information
Pages 115-132
Giulianella Coletti and Romano Scozzafava

Univariate statistical analysis with fuzzy data
Pages 133-147
Reinhard Viertl

Bootstrap approach to the multi-sample test of means with imprecise data
Pages 148-162
María Ángeles Gil, Manuel Montenegro, Gil González-Rodríguez, Ana Colubi and María Rosa Casals

A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing
Pages 163-176
Gil González-Rodríguez, Ana Colubi and María Ángeles Gil

A decision support system methodology for forecasting of time series based on soft computing
Pages 177-191
J.D. Bermúdez, J.V. Segura and E. Vercher

Data analysis with fuzzy clustering methods
Pages 192-214
Christian Döring, Marie-Jeanne Lesot and Rudolf Kruse

Extending fuzzy and probabilistic clustering to very large data sets
Pages 215-234
Richard J. Hathaway and James C. Bezdek

Regression with fuzzy random data
Pages 235-252
Wolfgang Näther

Dual models for possibilistic regression analysis
Pages 253-266
Peijun Guo and Hideo Tanaka

Least squares estimation of a linear regression model with LR fuzzy response
Pages 267-286
Renato Coppi, Pierpaolo D’Urso, Paolo Giordani and Adriana Santoro

Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable
Pages 287-313
Pierpaolo D’Urso and Adriana Santoro

The coefficient of concordance for vague data
Pages 314-322
Przemysław Grzegorzewski

Goodman–Kruskal γ measure of dependence for fuzzy ordered categorical data
Pages 323-334
Olgierd Hryniewicz

Fuzzy multidimensional scaling
Pages 335-359
Pierre-Alexandre Hébert, Marie-Hélène Masson and Thierry Denœux

I-Scal: Multidimensional scaling of interval dissimilarities
Pages 360-378
P.J.F. Groenen, S. Winsberg, O. Rodríguez and E. Diday

A comparison of three methods for principal component analysis of fuzzy interval data
Pages 379-397
Paolo Giordani and Henk A.L. Kiers

Design of local fuzzy models using evolutionary algorithms
Pages 398-416
Piero P. Bonissone, Anil Varma, Kareem S. Aggour and Feng Xue

Fuzzy modelling and estimation of economic relationships
Pages 417-433
David Shepherd and Francis K.C. Shi

Development of fuzzy process control charts and fuzzy unnatural pattern analyses
Pages 434-451
Murat Gülbay and Cengiz Kahraman

8. Old paper by Lotfi Zadeh

Toward a Generalized Theory of Uncertainty (GTU)—An Outline is the most up-to-date version of Zadeh's recent ideas available at the BISC website.

This paper appeared in Information Sciences 172 (2005), 1-40. If you have access to this paper via Sciencedirect, this version is a Word document with all the tables and figures at the end.

Additionally, you can download a few selected Zadeh papers here.

7. New edited volume (SMPS'06)

Springer has published the edited volume Soft Methods for Integrated Uncertainty Modelling containing the proceedings of the SMPS'06 (Soft Methods in Probability and Statistics) conference held at Bristol last month. Editors are J. Lawry, E. Miranda, A. Bugarin, S. Li, M.A. Gil, P. Grzegorzewski and O. Hryniewicz.

The last time I checked, the Springer website offered no TOC for this volume. You can find the titles and authors of the contributions here at the conference website.

Btw, the 4th SMPS will be Toulouse 2008.

6. Old paper by Brian Weatherson

This paper by philosopher Brian Weatherson is not about fuzzy sets but I find it relevant for foundational discussions with Bayesians. Weatherson presents a Dutch Book argument which works under intuitionistic logic. An obvious implication, good news for open-minded Bayesianism, is that commitment to classical logic is not necessary in order to adhere to De Finetti's view of probability. Another implication is that adherence to the Dutch Book cannot, in and of itself, rule out other logics.

In From classical to intuitionistic probability, a bet on the occurence of A can be settled for A, against A or remain unsettled (cf. a proposition in intuitionistic logic can be true, false or neither- if it hasn't been proved true or proved false).

Accordingly, Weatherson's intuitionistic probabilities allow for the probabilities of an event and its contrary to sum up to less than 1. Thus he presents them as an alternative to belief functions.

This paper appeared in Notre Dame Journal of Formal Logic 44 (2004), 111-123.

5. New paper by Agresti and Gottard

This paper elaborates on a suggestion made by Alan Agresti and Anna Gottard in their recent discussion of a paper by Geyer and Meeden in Statistical Science.

If you missed a non-fuzzy statistician suggesting a fuzzy p-value and having it discussed in a major Statistics journal, that proves something like this blog is needed.

The paper Reducing Conservatism of Exact Small-Sample Methods of Inference for Discrete Data is available as a Technical Report from the Università di Firenze. Update: To appear in Computational Statistics and Data Analysis.

You may also want to visit Charles Geyer's website.

4. Forthcoming special issue of CSDA

A special issue of Computational Statistics and Data Analysis is forthcoming on the topic The fuzzy approach to statistical analysis. Guest editors are Renato Coppi, Maria A. Gil and Henk A.L. Kiers.

The papers are already available via Sciencedirect at the journal's site (in the 'Articles in Press' section).

This is the first special issue on Fuzzy Sets ever to appear in a Statistics journal, and I expect this fact to arouse some reaction.

3. New special issue of FSS

Volume 157, issue 19 of Fuzzy Sets and Systems is a special issue on Fuzzy Sets and Probability/Statistics Theories. The guest editors are María Ángeles Gil, Miguel López Díaz and Dan A. Ralescu.

The table of contents is as follows:

Editorial
Page 2545
María Ángeles Gil, Miguel López Díaz and Dan A. Ralescu

Overview on the development of fuzzy random variables
Pages 2546-2557
María Ángeles Gil, Miguel López-Díaz and Dan A. Ralescu

On Borel measurability and large deviations for fuzzy random variables
Pages 2558-2568
Pedro Terán Agraz

Strong laws of large numbers for independent fuzzy set-valued random variables
Pages 2569-2578
Shoumei Li and Yukio Ogura

Least-squares estimation in linear regression models with vague concepts
Pages 2579-2592
Volker Krätschmer

A strong consistent least-squares estimator in a linear fuzzy regression model with fuzzy parameters and fuzzy dependent variables
Pages 2593-2607
Christoph Stahl

Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data
Pages 2608-2613
Gil González-Rodríguez, Manuel Montenegro, Ana Colubi and María Ángeles Gil

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty
Pages 2614-2626
Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami and Masami Kurano

Goodness of fit and variable selection in the fuzzy multiple linear regression
Pages 2627-2647
Pierpaolo D’Urso and Adriana Santoro

Two- and three-way component models for LR fuzzy data in a possibilistic framework
Pages 2648-2664
Paolo Giordani

Possibilistic decisions and fuzzy statistical tests
Pages 2665-2673
Olgierd Hryniewicz

A fuzzy approach to Markov decision processes with uncertain transition probabilities
Pages 2674-2682
M. Kurano, M. Yasuda, J. Nakagami and Y. Yoshida

2. Linz 2007

The 28th edition of the well-known Linz Seminar (February 2007) will be devoted to the topic Fuzzy Sets, Probability, and Statistics – Gaps and Bridges.

You can find all the information here. The deadline for submission is November 25, 2006, so you are still in time.

1. Editorial post & FAQ

If you don't know what a blog is, or if you bought the idea that blogging is just a form of alternative press, you might be missing a lot of fun. Essentially, a blog is a website with a predefined structure which is organized as a time-ordered sequence of entries. There are many imaginative blogs where this format, however limited it appears to be, has proved to be really useful for a specific purpose.

Advantages of blogging are:
-Minimal time consumption.
-Search ability incorporated.
-Readers' comments allowed.
-Immediate publication.

After a one-year satisfactory experience with my personal blog, the other day it suddenly dawned on me that blogs may be really useful to small, heterogeneous scientific communities. I guess I am a member of one such community: those interested in the interface area between Statistics & Probability and Fuzzy Set Theory. Trying to keep up with the developments takes me a lot of time spent on Internet searches, because:

-Papers are not published in a small number of core journals, but spread across journals belonging to Statistics, Mathematics, Computer Science and subject-matter studies.
-Papers are typically not posted on preprint servers like e.g. the arXiv.
-Papers are typically not available at the author's website because many authors (like me) just do not keep, or have the time to update, a website.

So it is just typical that I miss a paper by an author I follow closely; and I am certain to be constantly missing relevant research indirectly related to my own, even if I really commit an effort to the task.

Also, this type of research is young and objectively attracts increasing attention, so it is not easy for incoming authors to find the places to learn and master some basic techniques (lack of specialized texts for graduate students, and so on).

Moreover, although a vast effort has been devoted by some to dispelling a number of recurring misunderstandings and controversies with respected members of the Statistics community, the difficulty of scanning the literature makes some critics be less well-informed than I would wish them to be. Discussions in the scientific tradition of paper-response-rejoinder are slow and uneffective according to today's standards, and tend to bring ill-informed offspring for virtually unlimited time. Therefore it is only in our best interest to help critics to be as well informed as possible.

Finally, there is a foundational side to this research which naturally welcomes discussion. Interesting foundational papers are bound to appear at random and unpredictable places and are very easy to miss.

With this blog I will try to make a humble and personal but cost-effective contribution to mitigating the worse of that situation. I don't know whether any success will be achieved; maybe the blog will turn out to be not useful at all to my colleagues. We'll just see, but in that case the task will have been so inexpensive that the venture seems worth all the same.

Reading some entries should be self-explanatory about what I have in mind, but you are also invited to go on reading the FAQ or contact me in case of doubt.



Frequently Asked Questions

A more complete FAQ will appear here as soon as time allows.

What is the difference between your blog and a preprint server?
The blog does not host any files. It only contains links to preexisting web or ftp addresses.

I have written a very interesting preprint, will you write an entry about it?
Send me a link, I will check that the paper's topic is suitable and I will write the entry. If you send me also a short summary, I may use it or write my own.

Does that mean that only people with a website can contribute links to their work?
Not at all! Nowadays there are plenty of websites that will provide you with free file storage. It will only take you a couple of minutes to open an account and upload your file (PDF preferred). Do read the terms of service though, as some websites do not allow you to upload copyrighted material, or will claim copyright on whatever you upload, or will delete your file if it's not accessed for a long time. I personally use box.net, but I am not endorsing box.net in any way. Please feel free to write a comment suggesting better options.

What is the difference between your blog and a newsletter?
My idea is to be rather specific about information. If you are organizing a special session relevant to this blog I will inform about it, but don't expect me to inform about every single conference where one could potentially submit a SPFS.

Would you post a list of my papers?
Don't ask for it until you see here a list of my papers. But I would certainly post a list of links to your papers if they are available for free in the web (alternatively, a link to your website if that's more handy).

Will you be posting links to already published papers that are nowhere available for free?
Only very exceptionally, to say the least.

Are comments moderated?
Comments are not moderated and you can use the comments in imaginative ways (e.g. give news), but posterior deletion is technically feasible for the blog editor.

Will you remove upon request a comment that has outraged me?
Sigh, I hope this sort of situation will just not happen.

Are very long and technical comments, with parts in TeX, allowed?
It's better to build a PDF file, put it somewhere in the web and just link to it.

How can I contact you?
Follow the `View my complete profile' link in the right column, then in the left there is a link labelled `Send me an email' or something of that sort.

I have found a broken link. What should I do?
Just leave a comment stating the fact (with the entry number). I receive all comments in my email address.