Calibrated Bayes, an Alternative Inferential Paradigm for Official Statistics

I characterize the prevailing philosophy of official statistics as a design/model compromise (DMC). It is design-based for descriptive inferences from large samples, and model-based for small area estimation, nonsampling errors such as nonresponse or measurement error, and some other subfields like ARIMA modeling of time series. I suggest that DMC involves a form of “inferential schizophrenia”, and offer examples of the problems this creates. An alternative philosophy for survey inference is calibrated Bayes (CB), where inferences for a particular data set are Bayesian, but models are chosen to yield inferences that have good design-based properties. I argue that CB resolves DMC conflicts, and capitalizes on the strengths of both frequentist and Bayesian approaches. Features of the CB approach to surveys include the incorporation of survey design information into the model, and models with weak prior distributions that avoid strong parametric assumptions. I describe two applications to U.S. Census Bureau data.