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 the Akaike Information Criterion. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form of holistic pragmatism

Recent Observations of Betelgeuse and New Instrumentation at the ISI

The Infrared Spatial Interferometer (ISI) has been conducting mid-infrared observations of late-type stars for about 18 years. A long-term set of diameter measurements of Betelgeuse at 11.15 μm shows pronounced changes in the stellar size over time. These changes may arise from variations in the opacity of the environment immediately surrounding the star. New instrumentation is being developed to identify the composition and kinematics of the circumstellar environment of Betelgeuse, and of other late-type stars. A digital spectrometer-correlator is being built and tested that will enable visibility measurements on and off individual molecular spectral lines. Results from testing the spectrometer system are presented

Solutions to Some Open Problems from Slaney

In response to a paper by Harris & Fitelson, Slaney states several open questions concerning possible strategies for proving distributivity in a wide class of positive sentential logics. In this note, I provide answers to all of Slaney's open questions. The result is a better understanding of the class of positive logics in which distributivity holds

Bayesians sometimes cannot ignore even very implausible theories (even ones that have not yet been thought of)

In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied

Remarks on "Random Sequences"

We show that standard statistical tests for randomness of finite sequences are language-dependent in an inductively pernicious way