## 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…

## Numbers rule your world

Posted in Books, Statistics with tags , , , , , , , , , , , on February 22, 2010 by xi'an

Andrew Gelman gave me a copy of the recent book Numbers rule your world by Kaiser Fung, along with the comment that it was a nice book but not for us. I spend my “lazy Sunday” morning reading the book at the breakfast table and agree with Andrew on his assessment. (waiting for the  incoming blog review!). Numbers rule your world is unlikely to bring enlightment to professional or academic statisticians, but it provides a nice and soft introduction to the use of statistics in everyday’s life, to the point I would encourage my second and third year students to read it. It covers a few topics that are central to Statistics via ten newspaper-ised stories that make for a very light read, but nonetheless make the point. The themes in Numbers rule your world are

• variability matters more than average, as illustrated by queuing phenomena;
• correlation is not causation, but is often good enough to uncover patterns, as illustrated by epidemiology and credit scoring;
• Simpson’s paradox explains for apparent bias in group differences, as illustrated by SAT score differences between black students and white students;
• false positives and false negatives have different impacts on the error (here comes Bayes theorem!), depending on population sizes and settings, as illustrated by the (great!) case of cheating athletes and polygraph tests (with a reference to Steve Fienberg‘s work);
• extreme events may exhibit causes, or not, as illustrated by a cheating lottery case (involving Jeff Rosenthal as the expert, not the cheater!) and a series of air crashes.

The overall tone of Numbers rule your world is pleasant and engaging, at the other end of the stylistic spectrum from Taleb’s Black Swan. Fung’s point is obviously the opposite of Taleb‘s: he is showing the reader how well statistical modelling can explain for apparently paradoxical behaviour. Fung is also adopting a very neutral tone, again a major change from Taleb, maybe being even too positive (no the only mention is made of the current housing crisis in the pages Numbers rule your world dedicates to credit scoring comes in the conclusion, pp. 176-7). Now, in terms of novelty, I cannot judge of the amount of innovation when compared with (numerous) other popular science books on the topic. For instance, I think Jeff Rosenthal’s Struck by Lightning brings a rather deeper perspective, but maybe thus restricts the readership further…