Yes, there are topics other than the U.S. election . . . ‘Richard Sperling writes:

I’m having a little problem discerning the difference(s) between the parametric bootstrap and Monte Carlo simulation. I’d appreciate it if you would clarify the distinction.

This reminds me in grad school, when Raghu said that in the future, instead of saying “I took a sample of size n from a normal distribution” or whatever, he’d say “I took a bootstrap of size n . . .” and it would sound so much cooler.

The short answer is that I don’t think there’s any clear difference between bootstrapping and posterior simulation. It’s just a matter of emphasis. When you’re doing a parametric bootstrap, you’re simulating replicated data from a fitted model, and the next step would be to simulate parameters from the uncertainty in that model, i.e., the posterior distribution. In bootstrapping the assumption is that you can construct a reasonable point estimate.

I’ve used bootstrapping on occasion in my own work. In my thesis on positron emission tomography, I bootstrapped on the Poisson distribution of cell counts in order to estimate a variance component from measurement error: see my 1991 paper (with Alpert et al.) in the Journal of Cerebral Blood Flow and Metabolism). And, with Alessandra Casella et al., I bootstrapped votes in a study of student elections. I think there are a couple more examples that I can’t recall right now.