Descriptive probability
Glenn Shafer, Rutgers
Abstract: As the late Berkeley statisticians Leo Breiman (1928-2005) and David Freedman (1938-2008) taught us, most statistical models in the social sciences, especially regression models, are invalid. Their conclusions are at best descriptive.
Some sociologists and other applied statisticians have proposed treating these dubious regression studies as purely descriptive, refraining from significance tests and confidence statements. This is seldom done, because people want some sense of the precision of the regression parameters.
Descriptive intervals for parameter values can be obtained if we imagine parameter values betting against each other using Kelley betting. This allows us to interpret relative likelihood as relative predictive success. See the working paper at http://probabilityandfinance.com/articles/59.pdf.
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