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A Bayesian analysis of binary misclassification

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  • Bollinger, Christopher R.
  • van Hasselt, Martijn

Abstract

We consider Bayesian inference about the mean of a binary variable that is subject to misclassification error. If the error probabilities are not known, or cannot be estimated, the parameter is only partially identified. For several reasonable and intuitive prior distributions of the misclassification probabilities, we derive new analytical expressions for the posterior distribution. Our results circumvent the need for Markov chain Monte Carlo simulation. The priors we use lead to regions in the identified set that are a posteriori more likely than others.

Suggested Citation

  • Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "A Bayesian analysis of binary misclassification," Economics Letters, Elsevier, vol. 156(C), pages 68-73.
    • Handle: RePEc:eee:ecolet:v:156:y:2017:i:c:p:68-73
    DOI: 10.1016/j.econlet.2017.04.011
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    References listed on IDEAS

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    1. Aigner, Dennis J., 1973. "Regression with a binary independent variable subject to errors of observation," Journal of Econometrics, Elsevier, vol. 1(1), pages 49-59, March.
    2. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    3. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    4. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(4), pages 483-509, August.
    5. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    6. Anil Gaba & Robert L. Winkler, 1992. "Implications of Errors in Survey Data: A Bayesian Model," Management Science, INFORMS, vol. 38(7), pages 913-925, July.
    7. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    8. E. Rahme & L. Joseph & T. W. Gyorkos, 2000. "Bayesian sample size determination for estimating binomial parameters from data subject to misclassification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 119-128.
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    Citations

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    Cited by:

    1. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    2. Toru Kitagawa, 2011. "Inference and decision for set identified parameters using posterior lower and upper probabilities," CeMMAP working papers CWP16/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. James Marton & Stephen A. Woodbury, 2013. "Retiree Health Benefits as Deferred Compensation," Public Finance Review, , vol. 41(1), pages 64-91, January.
    4. Martijn van Hasselt & Christopher R. Bollinger & Jeremy W. Bray, 2022. "A Bayesian approach to account for misclassification in prevalence and trend estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 351-367, March.

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    More about this item

    Keywords

    Bayesian inference; Partial identification; Misclassification;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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