Tuesday, August 5, 2014

The 7 Pillars of Statistical Wisdom

Yesterday, Stephen Stigler presented the (ASA) President's Invited Address to an overflow, and appreciative, audience at the 2014 Joint Statistical Meetings in Boston. The title of his talk was, "The Seven Pillars of Statistical Wisdom".

I'd been looking forward to this presentation by our foremost authority on the history of statistics, and it surpassed my (high) expectations.

The address will be published in JASA at some future date, and I urge you to read it when it appears. In the meantime, here are the "seven pillars" - the supporting pillars of statistical science - with some brief comments:

1. Aggregation (Sums; Means) - The combination of observations. Information is created by suppressing information. Examples: the arithmetic mean; index numbers; least squares; non-parametric "smoothers".

2. Information (The √n Rule) - How can we measure the accumulation of information? Accuracy is related to the amount of data - but it doesn't increase linearly. Noted by de Moivre and by Laplace. Think about the usual central limit theorems.

3. Likelihood (MLE's; Testing) - The use of probability to calibrate inferences. p-values!

4. Intercomparison (Percentiles; t-statistics) - Comparisons based on differences among the data themselves (not against some external standard). ANOVA; the bootstrap.

5. Regression (Multivariate inference; Bayes' Theorem)

6. Design (ANOVA; Design-based inference) - Use of sample surveys & field trials. "Induction: reasoning from a sample taken at random to the whole lot sampled."

7. Residuals (Models & Model Comparison) - Residual plots as diagnostics; comparison of nested models; testing the significance of regression coefficients; parametric modelling.

Stephen's talk was rich with interesting historical pictures and snippets. All-in-all a great event!

1. Thanks for the summary. I also wrote a summary and included some personal thoughts at http://blogs.sas.com/content/iml/2014/08/05/stiglers-seven-pillars-of-statistical-wisdom/

2. His book is now out.