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Abstract:
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In a finite population inference, the interest centers on a summary, Q, of observables, U={U1,U2,.,UN}, on a well-defined population of N subjects (or establishments). A sample is drawn using a known probabilistic mechanism which results in an inclusion vector of dummy variables, I, of dimension N. In a randomization-based inference the observable U is treated as a fixed vector of constants and I as a random vector of dummy variables. On the other hand, a Bayesian approach treats both I and U as random. Given the nonresponse, measurement error, coverage error etc., some modeling type assumptions about U are being made, implicitly, partially and, rather, haphazardly. In this era of needing to mix survey and non-survey data (W), it is advantageous to fully embrace the models for (I,U,W) and still maintain the predictive inference focus on the non-sampled or the unobserved portion of the finite population. We will explore the role of models in survey inference and the strength of Bayesian approach in the finite population survey inference.
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