The philosophical significance of Stein’s paradox

Charles Stein discovered a paradox in 1955 that many statisticians think is of fundamental importance. Here we explore its philosophical implications. We outline the nature of Stein’s result and of subsequent work on shrinkage estimators; then we describe how these results are related to Bayesianism and to model selection criteria like AIC. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form of holistic pragmatism.