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I am actively involved in research that will lead to better methods and a better understanding of statistical inference. This research involves connecting two different areas in statistics: finite population sampling (a mainstay of public health) and Bayesian approaches for inference. The connection is via the role of identifiable units in the two frameworks. The theoretical development allows the increased accuracy of Bayesian estimators (best linear unbiased predictors) to be characterized, and parameter spaces with limited accuracy to be identified. This development is important since it clarifies the contribution that statistics can make when attempting to generalize from data. The application of these results is broad, ranging from applications in clinical trials, survey sampling, experimental design, to broader methodological research, and environmental health. The methods are applicable to studies where there is error in measurement, such as exposure assessments (such as low level radio frequency energy), spatial data, cluster randomized trials, and observational studies.