June 11, 2020
In D. Corfield and J. Williamson (Eds.) Foundations of Bayesianism, Kluwer Applied Logic Series, Kluwer Academic Publishers,Vol. 24, 19-36, 2001.
TECHNICAL REPORT R-284 July 2001
I turned Bayesian in 1971, as soon as I began reading Savage’s monograph The Foundations of Statistical Inference [Savage, 1962]. The arguments were unassailable: (i) It is plain silly to ignore what we know, (ii) It is natural and useful to cast what we know in the language of probabilities, and (iii) If our subjective probabilities are erroneous, their impact will get washed out in due time, as the number of observations increases.
Thirty years later, I am still a devout Bayesian in the sense of (i), but I now doubt the wisdom of (ii) and I know that, in general, (iii) is false. Like most Bayesians, I believe that the knowledge we carry in our skulls, be its origin experience, schooling or hearsay, is an invaluable resource in all human activity, and that combining this knowledge with empirical data is the key to scientific enquiry and intelligent behavior. Thus, in this broad sense, I am a still Bayesian. However, in order to be combined with data, our knowledge must first be cast in some formal language, and what I have come to realize in the past ten years is that the language of probability is not suitable for the task; the bulk of human knowledge is organized around causal, not probabilistic relationships, and the grammar of probability calculus is insufficient for capturing those relationships. Specifically, the building blocks of our scientific and everyday knowledge are elementary facts such as “mud does not cause rain” and “symptoms do not cause disease” and those facts, strangely enough, cannot be expressed in the vocabulary of probability calculus. It is for this reason that I consider myself only a half-Bayesian.
In the rest of the paper, I plan to review the dichotomy between causal and statistical knowledge, to show the limitation of probability calculus in handling the former, to explain the impact that this limitation has had on various scientific disciplines and, finally, I will express my vision for future development in Bayesian philosophy: the enrichment of personal probabilities with causal vocabulary and causal calculus, so as to bring mathematical analysis closer to where knowledge resides.