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Subjective Bayesian Analysis for Surveys with Missing Data

Joseph B. Kadane
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 42, No. 4, Special Issue: Conference on Practical Bayesian Statistics, 1992 (1993), pp. 415-426
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2348475
Stable URL: http://www.jstor.org/stable/2348475
Page Count: 12
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Subjective Bayesian Analysis for Surveys with Missing Data
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Abstract

Almost every survey has missing data, sometimes because of inadequacy of the sampling frame, sometimes because of the unwillingness of persons in the frame to participate, sometimes because of the inability of the surveyors to find everyone in the frame, and usually because of an unknown mixture of all these reasons and others. The analyses of surveys often ignore the missing data, treating it as a complete sample of those who responded. However, to do this is often to assume away the principal source of uncertainty, rendering statements of uncertainty conditioned on that assumption problematic. One solution is the assumption of 'ignorability', as discussed by Don Rubin. This approach essentially states in conditional probability terms what one must assume, to get away with an analysis that does not take into account the missing data. The purpose of this paper is to explore a second approach, in which differing beliefs about what the missing data would have been had they been collected are explored to see how robust the results of the survey are. What is reasonable to assume depends on subjective judgements of the analyst. These ideas are considered in the context of a survey on juror death penalty attitudes and behavior.

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