A Case Study of the Robustness of Bayesian Methods of Inference: Estimating the Total in a Finite Population Using Transformations to Normality

Publisher Summary This chapter presents a case study of the robustness of Bayesian methods of inference estimating the total in a finite population using transformations to normality. Bayesian intervals provide interval estimates that can legitimately be interpreted as such or at least to offer guidance as to when the intervals that are provided can be safely interpreted in this manner. The potential application of the statistical methods is often demonstrated either theoretically, from artificial data generated following some convenient analytic form, or from real data without a known correct answer. The case study presented here uses a small, real data set with a known value for the quantity to be estimated. It is surprising and instructive to see the care that may be needed to arrive at satisfactory inferences with real data. Simulation techniques are not needed to estimate totals routinely in practice. If stratification variables were available, that is, categorizing the municipalities into villages, towns, cities, and boroughs of New York City, to estimate the population total from a sample of 100, oversampling the large municipalities would be highly desirable. Robustness is not a property of data alone or questions alone, but particular combinations of data, questions and families of models. In many problems, statisticians may be able to define the questions being studied so as to have robust answers.