Models of Data Generation vs. Models of Events that Generate Data

Abstract

Let me begin by describing a very general model of a data-generating process. An experimental psychologist studying human decision making decides to obtain data bearing on some hypothesis or other. To record these data, he prepares a blank contingency table with its compartment-defining boundaries and internal subdivisions in place, but with no observations recorded. As data collection proceeds, the cells of the table provide loci for recording the data. By counting the tallies, he can assess numbers that seem to be useful estimators of various probabilities, and ratios of such numbers that are often even more useful. I shall call this blank table the “statistician’s model of data.” The underlying notion is that a data-generating process produces the observations, and we use those observations to infer properties of that process. This model is as appropriate to what Bayesian statisticians do as to what classical ones do. Nothing important changes if we deal with continuous rather than discrete observations — measures rather than counts.