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A mixture model for rounded data

Wright, David E.; Bray, Issy


David E. Wright

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Issy Bray
Associate Professor in Public Health (Epidemiology)


The paper focuses on the problem of data heaping that arises when measurements are recorded to varying degrees of precision. The work is motivated by an application in foetal medicine where measurements obtained from ultrasound images are rounded to varying numbers of decimal places causing heaping at integer values. We demonstrate the dangers of ignoring heaping before presenting a case-study of the ultrasound measurements. A mixture model, in which the different components represent different levels of rounding, is used for the heaping process. We illustrate a range of graphical posterior predictive checks to assess the fit of the model and we explore some extensions of the model. We adopt a Bayesian approach implemented by using the Gibbs sampler.


Wright, D. E., & Bray, I. (2003). A mixture model for rounded data. Journal of the Royal Statistical Society: Series D, 52(1), 3-13.

Journal Article Type Article
Publication Date Mar 3, 2003
Journal Journal of the Royal Statistical Society: Series D (The Statistician)
Print ISSN 0039-0526
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 52
Issue 1
Pages 3-13
Keywords bayesian statistics, coarsened data, heaping, Markov chain, Monte Carlo methods, quantile–quantile plots, residual plots, ultrasound
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