Thursday, November 22, 2007

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.

Thursday, November 15, 2007

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!)

Wednesday, November 14, 2007

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!

Tuesday, November 13, 2007

35. Copula wiki website

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

Monday, November 12, 2007

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. Update: AoS 37 (2009), 3059-3097.

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.

Thursday, November 08, 2007

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