http://www.b-eye-network.com/view/9947
(Laughing) I’ve always been a Bayesian; it’s Bayes practitioners that scared me. The Bayes movement is much more grounded now than it was 25 years ago. There seems to be more of a connection with real world problems and data, an evolution from subjective to objective. The tension between frequentists and Bayesians is not what it was years ago when Bayesians seemed too credulous. The competition between Bayesians and frequentists in real world applications should advance both, to the benefit of science and business.
Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors is much smaller than the number of observations. Modern scientific devices often reverse this scenario. A microarray analysis, for example, might include N = 100 subjects measured on p = 10000 genes, each of which is a potential predictor. An empirical Bayes approach where the prediction rule is estimated using data from all attributes might be optimal.
It’s pretty clear to me that statistics will play an increasing role helping 21st century sciences like biology, economics and medicine handle their large and messy data problems, and that an integration of frequentist and Bayesian approaches is probably ideal for meeting those data challenges.
One of the main responses of Bayesians to the objectivity demanded by frequentists is “uninformative priors” that are devoid of specific opinions. And the bootstrap, initially developed from a purely frequentist perspective, might provide a simple way of facilitating a genuinely objective Bayesian analysis. Though still suggestive, the bootstrap/priors connection merits further investigation.
Empirical Bayes combines the two statistical philosophies, estimating the “priors” frequentistically to carry out subsequent Bayesian calculations. Bayes models may prove ideal for handling the massively parallel data sets used for simultaneous inference with microarrays, for example. The oft-repeated structure of microarray data is just what is needed to make empirical Bayes a suitable approach.
I’m now prepping for a talk on "The Future of Indirect Evidence" that builds on the "Learning from the Experience of Others" presentation you attended. How is it, for example, that baseball player batting averages over the first month of the season can be used as reliable predictors of final season averages, and that Reed Johnson’s month one stats can help estimate Alex Rodriquez’s final season average? The answer lies in a statistical theorem that says the James-Stein empirical Bayes estimator beats the observed averages in terms of total expected squared error. Perhaps player agents can find use in that.
