What question did this study set out to answer?

To formulate a general statistical model for coarsened data and determine the exact conditions required to ignore the coarsening mechanism during inference.

December 1, 1991The Annals of StatisticsOpen Access

Ignorability and Coarse Data

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To formulate a general statistical model for coarsened data and determine the exact conditions required to ignore the coarsening mechanism during inference.
Constructed a general mathematical framework defining coarse observations as subsets within the power set of a target random variable's sample space, encompassing rounded, heaped, censored, and missing data.
Formulated the 'coarsened at random' (CAR) condition as an extension of 'missing at random' (MAR), evaluated alongside parameter distinctness between the data-generating and coarsening mechanisms.
Applied the ignorability framework to analytical proofs, numerical examples, and various observational data settings.
Established mathematically that the stochastic process driving coarsening can be ignored during Bayesian and likelihood inference if data are coarsened at random and parameters are distinct.
Demonstrated that satisfying these ignorability conditions allows coarsened data to be validly analyzed using standard methods for grouped data without modeling the coarsening mechanism directly.

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Implication

Methodological analysis reveals criteria for ignorability in coarse data, suggesting valid likelihood and Bayesian inferences without modeling stochastic coarsening processes.

Cite This Study

Heitjan et al. (1991) studied this question.

synapsesocial.com/papers/6a0fe3f992676d5461fd3610 https://doi.org/10.1214/aos/1176348396

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Implication

Methodological analysis reveals criteria for ignorability in coarse data, suggesting valid likelihood and Bayesian inferences without modeling stochastic coarsening processes.

Ignorability and Coarse Data

Key Points

Discussion

Implication

Cite This Study

Ignorability and Coarse Data

Key Points

Discussion

Implication

Cite This Study

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