Señor Redcardo Clark Schweinsteiger, I was also saddened to hear of the passing of Manute Bol. The poster in our elementary school gym that still resonates with me is the one that said “Don’t say I can’t, say I can’t yet.”
Here are some two-dimensional embeddings (PCA left, Isomap right) of FIFA World Cup squad heights, first taking features to be the counts of the discrete-valued heights (there are 36 different heights in the rosters; these features are essentially probability mass functions)
and second, taking features to be cumulative distribution functions
With the cdf features, in both embeddings the first component (the dimension shown left to right) is essentially the average height. I have no interpretation for the embedded pdf features. The Isomap embedding with the cdf features shows interesting structure, although I don’t see anything related to team performance. Working with the cdf features seems to make better sense than working with the pdf features.
The origins of statistics in biometry, eugenics, etc. is certainly an interesting history. I recently attended a seminar given by Sastry Pantula in his role as president of the American Statistical Association (ASA), in which he talked about growth, impact, visibility, and education initiatives of the association. One interesting point that came up was that professional statisticians are discouraging the AP Statistics course offered in high schools. Also, apparently, Pantula shows an IBM commercial whenever he gives his spiel about the ASA, a commercial like this one:
Statistics has really come a long way since its origins and some of it is very mathematical—some would say too mathematical. Regarding statistics, Jerome Friedman wrote more than a decade ago, “If we are to compete with other data related fields in the academic (and commercial) marketplace, some of our basic paradigms will have to be modified. We may have to moderate our romance with mathematics. Mathematics (like computing) is a tool, a very powerful one to be sure, but not the only one that can be used to validate statistical methodology. Mathematics is not equivalent to theory, nor vice versa. Theories are intended to create understanding and mathematics, although quite valuable, is not the only way to do this. For example, the germ theory of disease (in and of itself) has little mathematical content, but it leads to considerable understanding of much medical phenomena. We will have to recognize that empirical validation, although necessarily limited (as is mathematics), does constitute a form of validation.” Interesting stuff that I agree with. It seems to me that the new field going by the name analytics is taking over the commercial marketplace (if it hasn’t already). For example, Steve LaValle recently said that “in top-performing organizations, analytics has replaced intuition as the best way to answer questions.”
There is another related romance that I think has blossomed in fields such as information theory, theoretical computer science, signal processing, and statistics, which is described here by several prominent theoretical computer scientists. “1. Assignment of little weight to ‘conceptual’ considerations, while assigning the dominant weight to technical considerations. 2. The view that technical simplicity is a drawback, and the failure to realize that simple observations may represent an important mind-switch that can pave the way to significant progress.”
Is this sort of thing an inevitable part of the evolution of fields of study? For any field could you say that it hasn’t happened, or only that it hasn’t happened yet?