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January 11, 2007
Distribution of statisticial techniques
After several years I have looked at Brad Efron's R. A. Fisher in the 21st century. He provides an interesting chart of statistical techniques:
Another interesting chart is the following description of the different ideals that each school in statistics is pursuing:
Many readers might already be familiar with the frequentist and the Bayesian ideologies, but the fiducial approach is often a bit of a mystery. I like to explain as an analytic version of parametric bootstrap: assume that θ is the ML parameter estimate; now draw samples of the same size from θ, and do a ML estimate on each of them. This way you will obtain a distribution of θ-reestimates with a very similar function as the posterior distribution of θ had one adopted the Bayesian approach. I dislike the fact that we 'guess' the ML estimate of θ in the first place, however, and then proceed by assuming that it is true.
Posted by Aleks at January 11, 2007 9:33 AM
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Comments
Aleks,
Efron is always interesting but I disagree with these charts for many many reasons. Two quick examples:
- It does not make sense to put "Gibbs sampler," which is a computational technique) in parallel with "partial likelihood" (for example). I think this sort of characterization can only make sense if you start by separating statistical, mathematical, and computational ideas.
- I completely disagree with the association of Bayes with individual decisions. This is what Savage wrote about, but it's not the Bayesian data analysis that I know.
Posted by: Andrew Gelman at January 12, 2007 1:31 AM.
It is also not (meant to be) historically accurate - for instance Fisher worked extensively on meta-analysis topics.
Keith
Posted by: Keith O'Rourke at January 15, 2007 9:09 AM.