Inference under informative sampling

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Bayesian Estimation Under Informative Sampling (2015, methodology): “Although our method utilizes the weights as a “plug-in”, rather than imposing a prior, Pfeffermann & Sverchkov (2009) use Bayes rule to demonstrate one may replace the weights with their conditional expectation given the observed response to correct for informative sampling.”
Are Survey Weights Needed? A Review of Diagnostic Tests in Regression Analysis (2016, background): “As noted in Section 2, Pfeffermann & Sverchkov (2009) provide a key result here.”