Seymour Geisser

In most statistics departments, there is an enormous emphasis on testing hypotheses and estimating parameters in courses on statistical inference and applied statistics. I firmly believe that this emphasis is largely misplaced because it fosters the illusion that so-called statistical hypotheses completely reflect the scientific possibilities or critical physical mechanisms, and that parameters are always existent entities. For most situations this is simply not true. We look at a set of potential frameworks and choose the one that best suits our needs, although we are fairly certain that the one chosen is not the true one. The proper term for this activity is "model selection," and most often it is done with a particular purpose in mind--namely, predicting future observables generated from the process under scrutiny. Predictivism, which directs inference and decision toward potential observables (whether in the past or future), thus deserves at least as prominent a place in statistical theory and practice as estimation. A major technical difference between prediction and estimation, as I see it, is that prediction uses inferences (preferably framed probabilistically) about a finite number of unobserved values, whereas estimation, aside from inferring about the possible values of a physical constant, pertains either to a function of an infinite number of hypothetical observables or to a completely unobservable and possibly nonexistent entity. It seems to me that the finite number should take precedence in statistical instruction and application, since, in this sense, estimation is a limiting case of prediction. My research has been directed toward implementing this philosophical stance wherever statistics can be applied in univariate and multivariate problems. This includes problems of comparisons, model selection, classification, diagnostics, calibration, regulation, the proportion of values falling in a defined set, growth curves, discordancy assessment, perturbation analysis, robustness, and sample reuse. My work has been supported at various times by the U.S. Army, the National Science Foundation, and the National Institutes of Health.