SOME REMARKS ON STATISTICS AND SCIENTIFIC EXPLANATION

Probability and statistics, as quantitative reasoning tools, determine and are affected by the experimental context. Because reasoning and the communication of reasoning are encoded by one's language, it is surprising that the interplay be- tween statistical reasoning and the language of explanation of natural phenomena is less frequently discussed. In biomedical applications, for example, investigators formulate questions about a biological phenomenon (ω) and observe data X = x in accordance to an experimental protocol M (i.e., experimental design, sampling units, measurement scales, etc). Statisticians then return a statement ˆ θ about an abstract parametric structure θ describing a probability law of X, or certain func- tions of it. The interplay among the language expressing the investigator's initial question about ω, the experimental protocol M and the statistician's language reporting the resulting inferences about θ (or X) often goes unsuspected. In the following, we briefly comment on explanation and prediction in science, and then concentrate on a few remarks related to our main theme: Increased consideration should be given to the consequences of the fact that the practice of statistics and probability both determines and is affected by the collective of many different cul- tures of scientific enquiry and corresponding collective of experimental protocols. The goal of a unity of scientific explanation, we argue, will serve to a better under- standing of the domain and adequacy of a forcible view of probability and statistics in science. Explanation in science. John Casti and Anders Karlqvist (1991) suggest that the purpose of science is to provide explanation of perceived events (ω )a nd to en- large such explanations with predictions of what future events will be seen next. What distinguishes scientific from other methods is explanation and prediction by rule, characterized by its explicit and public character. Because rules are explicit, they can be taught and used by anyone after appropriate training. Because they are public, they are open to common scrutiny regarding their validity and effectiveness for prediction and explanation of natural events. Of importance to the statistician's dialogue in collaborative projects is learning that the distinction between explana- tion and prediction can only be appreciated by considering how different corners of science have dealt with each one of them (e.g., explanation by reductionist princi- ples of physics and chemistry in cell biology and the prediction of its evolutionary complexity, reduction vs. synthesis).