The fundamentals of statistical inference—frequentist, Bayesian, Fisherian —were set in place by the end of the first half of the twentieth century, as discussed in Part I of this book. The postwar era witnessed a massive expansion of statistical methodology, responding to the data-driven demands of modern scientific technology. We are now at the end of Part II, “Early Computer-Age Methods,” having surveyed the march of new statistical algorithms and their inferential justification from the 1950s through the 1990s.

This was a time of opportunity for the discipline of statistics, when the speed of computation increased by a factor of a thousand, and then another thousand. As we said before, a land bridge had opened to a new continent, but not everyone was eager to cross. We saw a mixed picture: the computer played a minor or negligible role in the development of some influential topics such as empirical Bayes, but was fundamental to others such as the bootstrap.

Fifteen major topics were examined in Chapters 6 through 13. What follows is a short scorecard of their inferential affinities, Bayesian, frequentist, or Fisherian, as well as an assessment of the computer's role in their development. None of this is very precise, but the overall picture, illustrated in Figure 14.1, is evocative.

Empirical Bayes

Robbins’ original development of formula (6.5) was frequentistic, but most statistical researchers were frequentists in the postwar era so that could be expected. The obvious Bayesian component of empirical Bayes arguments is balanced by their frequentist emphasis on (nearly) unbiased estimation of Bayesian estimators, as well as the restriction to using only current data for inference. Electronic computation played hardly any role in the theory's development (as indicated by blue coloring in the figure). Of course mod-ern empirical Bayes applications are heavily computational, but that is the case for most methods now.

James–Stein and Ridge Regression

The frequentist roots of James–Stein estimation are more definitive, especially given the force of the James–Stein theorem (7.16). Nevertheless, the empirical Bayes interpretation (7.13) lends James–Stein some Bayesian credibility. Electronic computation played no role in its development.