Well this looks … interesting
(My impression of Taleb is that he says things I tend to agree with but in a blustery, overconfident, and overly long-winded way; this document looks appealing because it has actual math and that might help overcome those problems)
(ETA: The “INCERTO” is apparently Taleb’s collective term for his four popular [non-mathematical] books)
Karol Borsuk is most famous for the Borsuk-Ulam theorem, discussed in his ground-breaking paper Drei Sätze über die n-dimensionale euklidische Sphäre. The same paper also mentions the following conjecture:
Can every bounded subset of the space Rn be partitioned into (n+1) sets, each of…
(via sometheoryofsampling)
The new time pattern for Petrarch’s love is shown in Fig. 4 together with the grades given by Jones to the 23 dated poems (see Fig. 1); obviously, I have assumed that the grade is proportional to Petrarch’s love. The fit is very good – actually, as good as that which is usually obtained when calibrating models of electrical and mechanical systems. Moreover, the fit could be further improved by slightly modifying the parameter values. But I do not show results along this line, because I do not want to give the impression that I believe that Petrarch had been producing his lyrics like a rigid, deterministic machine.
Just remembered for the first time in years one of the oddest applied math papers I’ve ever read, one that created an ordinary differential equation model of the relationship of Petrarch and his lover Laura over time, as reflected in Petrarch’s poetry (PDF link)
(via ordinalitis)
Hmm, I’m not sure I’ve heard that story, though it doesn’t surprise me — I’ve also heard some bad shit about his relationship with Matthew Cook, the research assistant who actually proved that Rule 110 was Turing complete (one of the big ideas presented in A New Kind of Science)
See Shalizi’s review*, which also contains a bit about Shalizi’s own run-in with Wolfram
*if you’re wondering, yes, it does worry me sometimes just how much of my information I get from Cosma Shalizi, who is just one guy — on the other hand he has written about many interesting things, and seems trustworthy when his writing overlaps with my areas of prior knowledge
For really quick conceptual background, the opening of Shalizi’s notebook on the subject (the part before the recommendations).
I’ve been reading Glymour’s book “The Mind’s Arrows: Bayes Nets and Graphical Causal Models in Psychology,” which provides an introduction to these methods in the service of discussing their relevance to psychology. It’s pretty accessible, given basic probability knowledge like “conditional probability” and “independence.” Glymour’s prose in the book is also much more lucid than in the paper that’s been discussed (although, confusingly, the last chapter of the book is a nearly unedited version of that very paper).
My university library had a digital copy of this book, which I have downloaded (except for the first few pages of one chapter which were mysteriously missing). If desired, it is conceivable that PDFs could appear in some email inboxes for completely mysterious reasons.
If you want more technical information about these methods, in particular how to discover causal structure (“search”), the book Causation, Prediction and Search by Spirtes, Glymour and Scheines seems like the standard reference. Shalizi has written some brief notes that discuss search algorithms here, as part of the lecture notes for a Data Mining class.
If you want to play around with real code and data, the TETRAD program is available here.
The IQ debate has now metastasized to Slate Star Codex via a pretty good post from Scott about what one should do in response to mathematical arguments one does not understand.
I had a quibble with the post’s framing which I mentioned here.
The comments thread is typical of SSC comments threads in that its highs are high and its lows are very, very low. The highs include some comments by Ilya Shpitser, who actually works in causal inference stuff for a living. Since Shpitser seems to broadly agree with me, and has far more knowledge in the relevant fields, I think you can probably assume that his contributions to the conversation will be strictly better than mine.
In one part of the thread, Shpitser argues with someone who says that causal inference stuff a la Glymour and Pearl is not useful in practice. Since I’ve generally tended to trust the people who say that it is useful (or that when it is useless, nothing else is useful), I’m very interested to see how this one shakes out.
The lowest of the lows is a commenter who – appearing to treat correlation as though it is close to being deductive implication – assures Scott that all personal experience aside, he is almost certainly not bad at math, because he is an Ashkenazi Jew, then goes on to accuse Clark Glymour of having no idea what the technical term “vanishing tetrad” means because they (the commenter) has never heard of it, and Glymour is a philosophy professor. (Converting one’s own lack of sub-field expertise into ability to judge other people’s sub-field expertise is a pretty neat trick.)
SSC comments never disappoint!
Recent fiddling around in Bayesland has led me to think
The main themes are that (1) many parameters are only very poorly identified with credible assumptions, due to the ubiquity of missing data; but (2) non-trivial partial-identification bounds, based on not-too-strong assumptions, do exist; while (3) the traditional assumptions used to point-identify parameters (e.g., linear homogeneous demand-and-supply curves in economics, plus instrumental variables) are very strong, sometimes completely unfalsifiable, and have little or no basis in established or even conjectural theory. Finally, (4) it is important for both social science and policy to admit to the uncertainty or ambiguity this leaves us with, rather than simply making stuff up so as to be definite.
(Cosma Shalizi, review of Identification for Prediction and Decision by Charles F. Manski)