Steven McKinney, Ph.D.
Molecular Oncology and Breast Cancer Program
British Columbia Cancer Research Centre
On Bradley Efron’s: “Frequentist Accuracy of Bayesian Estimates”
Bradley Efron has produced another fine set of results, yielding a valuable estimate of variability for a Bayesian estimate derived from a Markov Chain Monte Carlo algorithm, in his latest paper “Frequentist accuracy of Bayesian estimates” (J. R. Statist. Soc. B (2015) 77, Part 3, pp. 617–646). I give a general overview of Efron’s brilliance via his Introduction discussion (his words “in double quotes”).
The past two decades have witnessed a greatly increased use of Bayesian techniques in statistical applications. Objective Bayes methods, based on neutral or uniformative priors of the type pioneered by Jeffreys, dominate these applications, carried forward on a wave of popularity for Markov chain Monte Carlo (MCMC) algorithms. Good references include Ghosh (2011), Berger (2006) and Kass and Wasserman (1996).”
A nice concise summary, one that should bring joy to anyone interested in Bayesian methods after all the Bayesian-bashing of the middle 20th century. Efron himself has crafted many beautiful results in the Empirical Bayes arena. He has reviewed important differences between Bayesian and frequentist outcomes that point to some as-yet unsettled issues in statistical theory and philosophy such as his scales of evidence work. Continue reading