Conceptualistic Pragmatism: A framework for Bayesian analysis?

Abstract

This paper argues for an extended framework for the subjectivist approach to statistical decision making—the judgements made for deriving a likelihood function should be carefully reflected upon. The Harvard professor of philosophy Clarence I. Lewis did offer a philosophical action-oriented framework for this type of reflection. The philosophy of Lewis has very much influenced the originators of the quality movement. This constitutes an interesting link between two important learning-oriented approaches in the current statistical discourse—the subjectivist theory of statistical inference and the quality movement with its focus on continuous improvements.

Keywords:

• Subjective probability
• Bayesian
• Total Time on Test
• predictability
• in statistical control
• assignable causes
• pragmatism
• reflection
• judgements
• action

Acknowledgements

I am very much obliged to the mentorship concerted by Dick Barlow in my early career as a reliability engineer at Saab Aerospace in Linköping, Sweden, as an external PhD student at the Mathematical Statistics Department at Lund University, and later as a researcher on the statistical theory of reliability, see e.g., Bergman (1985). Not only did Dick pose some problems his research group at UC Berkeley had wrestled with and which I was fortunate enough to succeed in solving (see e.g., Bergman, 1977), but he also re-introduced me to the importance of the subjectivist approach. In fact, I had already in my philosophy studies prior to the mathematical statistics studies became acquainted with the work of Savage. However, to the despair of Dick, as an industrial statistician I kept a rather pragmatic stance to inference theory—it might be that this paper has become some sort of excuse for that approach. It is not only as a professional researcher that Dick became a mentor, e.g., he introduced me to the work of Dawkins (1976) which has very much affected my general world view. And I very much appreciate our friendship and all the enjoyable moments we have shared together—this extends also to our respective wives, Barbara and Elisabeth.

I also would like to thank an anonymous reviewer for many helpful comments. I also appreciated helpful comments and support from my colleagues at the Reliability Group of Gothenburg Mathematical Modelling Centre (GMMC). Support from the Swedish Foundation for Strategic Research to the GMMC and from SKF to the Division of Quality Sciences are gratefully acknowledged.