Archive for induction

Le Monde puzzle [#822]

Posted in Books, Kids, R with tags , , , , , , on June 10, 2013 by xi'an

For once Le Monde math puzzle is much more easily solved on a piece of paper than in R, even in a plane from Roma:

Given a partition of the set {1,…,N} in k groups, one considers the collection of all subsets of  the set {1,…,N} containing at least one element from each group. Show that the size of the collection cannot be 50.

Obviously, one could consider a range of possible N’s and k’s and run a program evaluating the sizes of the corresponding collections. However, if the k groups are of size n1,…,nk, the number of subsets satisfying the condition is

(2^{n_1}-1)\times \ldots \times (2^{n_k}-1)

and it is easily shown by induction that this number is necessarily odd, hence the impossible 50.

Quote-unquote

Posted in Books, Statistics with tags , , on January 2, 2011 by xi'an

“From the subjective standpoint, no assertion is possible without a priori opinion, but the variety of possible opinions makes problems depending on different opinions interesting.” Bruno de Finetti, 1951

Yesterday, I received this email:

I’m checking the following reference de Finetti, B. (1972) Probability, Induction and Statistics. J. Wiley, New York in your book Bayesian Choice 2nd edition (on the pages 46, 115, 160, as mentioned in author index). But I don’t see this reference is cited on any of the three pages. Would you please check if this de Finetti’s book is cited somewhere in your book or it actually should not appear in the bibliography?

I don’t see any review on amazon about this Finetti’s book. Since this book is cited in your book, I want to see how you describe this book. In any case, if you are familiar with this book, would you please comment a little bit on it? For example, what are important points from this book that are still relevant today?

to which I replied that

…indeed Probability, Induction and Statistics should not appear in the reference list of Bayesian Choice: I have read though parts of Theory of Probability vol. 1 (which is quoted on page 115) but I am not familiar with this other book which dates from 1955 (Italian version). Maybe you could look at Cifarelli & Regazzini’s survey of Bruno de Finetti’s work (Statistical Science, 1996, 11(4), 253-282) for a detailed coverage of the work.

Reading from this survey (and following Dennis Lindley’s advice), this book could be another topic for my advanced lectures at CREST but it will have to wait a few years, until I am satisfied with my coverage of Jaynes’s Probability Theory.

About induction, deduction, and transduction

Posted in Statistics with tags , , , , , , , on March 10, 2010 by xi'an

I have noticed a new posting by Ya’acov Ritov on arXiv that discusses what the limits of the scope of Statistics should be:

“The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality inference based on observational data.”

I do not have currently enough free time to read it at a detailed enough level to make a sensible comment, but this sounds like an interesting discussion! At this stage, I cannot decide whether this is yet again a point about model shifts or if there is a more fundamental issue at stake. (Thankfully, Popper is not mentioned! But Taleb is…) It seems however that the paper claims that prediction about a single object is not statistically valid:

“We believe that predicting the future, that is, predicting one most important future event, is not a statistical task.

and thus that statistics requires a long sequence of experiments to achieve validation, hence falling upon a frequentist justification…

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