Three-Toed Sloth

The Bootstrap

My "Computing Science" column for American Scientist, "The Bootstrap", is now available for your reading pleasure. Hopefully, this will assuage your curiosity about how to use the same data set not just to fit a statistical model but also to say how much uncertainty there is in the fit. (Hence my recent musings about the cost of bootstrapping.) And then the rest of the May-June issue looks pretty good, too.

I have been reading American Scientist since I started graduate school, lo these many years ago, and throughout that time one of the highlights for me has been the "Computing Science" column by Brian Hayes; it was quite thrilling to be asked about being one of the substitutes while he's on sabbatical, and I hope I've come close to his standard.

After-notes to the column itself:

• Efron's original paper is now open access.
• Of course, the time series is serially dependent, so I should really use a bootstrap which handles that, as in Künsch. Using either a moving block bootstrap or stationary bootstrap actually gave almost the same confidence bands as the one in the article, obtained by resampling consecutive pairs (perhaps because the optimal block length, selected per Lahiri, was just 4). The original version of the column went into that, but it had to be cut to fit the space.
• A bigger issue is that the data set is really not stationary. Like everyone else, I pretend.
• Originally, I wanted to use turbulent flow time series for the example, since it turns out that they are actually pretty well predicted by linear models, once you allow for very non-Gaussian driving noises. But I couldn't find any suitable data sets which wouldn't involve some tricky work to get permissions; perhaps I just didn't look in the right places. So I fell back on something which is publicly available, even though it's from a domain which if anything has gotten too much attention from statisticians and probabilists, and required some disclaimers.

Enigmas of Chance; Self-Centered