Last week's blog introduced Bayes theorem for conditional probability and contrasted the Bayesian and frequentist approaches in modern statistics, noting that the frequentist camp dominated when I studied 30 years ago. Now, however, though frequentism is still on top, the playing surface is much more level, with a steeper trajectory for Bayes.

There are a host of reasons for the ascent of Bayesian methods in recent generations. First is the increasing demand for applied statistical analysis – and new techniques – in the engineering, biological, epidemiological, social, physical, mathematical, computer and business sciences. Second is an evolution in statistical emphasis from scientific inquiry to organizational decision-making. Often as not, applied statisticians are now evaluated by the ability of their models to predict into the future. Other things equal, models that predict well are often preferred to those that explain well. Third are advances in computation and numerical methods that can now closely approximate what was many times intractable Bayesian calculation in the past. Fourth is the evolution in Bayesian analysis itself. Now, “empirical Bayes” replaces the subjective priors so disdained by frequentists with “uninformative priors” computed from data. Indeed, in many ways the empirical Bayes branch looks a lot like traditional frequentist methods.

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