| Popis: |
Bayesian analyses are often critiqued on the basis of dubious exchangeability claims regarding the data. Not only must observed data be exchangeable, but prior ``data'' must be as well, and the observed data must also be exchangeable with the prior data--an assumption not typically justified by the practitioner. Yet social scientists often utilize social data--observed human behaviors that rely on human judgment--to make inferences. Social priors shared by the researcher are, therefore, non-exchangeable with social data. One common defensive argument offered by Bayesian practitioners is that as long as there is some component of new information in the observed data, repeated observation-updating cycles will still eventually produce a highly informative posterior distribution. In frequentist statistics we have power analyses--a way of estimating how much data we need to get desirable properties from our estimator. Here I develop a model that parameterizes the degree of non-exchangeability between the observed data and the prior data and offers a standard way to calculate how many observations are needed to achieve a parameterized definition of an "informative" Bayes' estimate in a single iteration of updating, or the number of updating iterations needed given a fixed observation size n at each iteration. I illustrate the phenomenon with a combination of real and model-synthesized data showing how New York police officers who make stops learn from social data---convictions generated by jury trials in the U.S. justice system. |
