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A bayesian solution to reconstructing centrally censored distributions

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Abstract

Bayesian methods are investigated for the reconstruction of mixtures in the case of central censoring. Earlier literature suggested that when the relationship between a continuous and a categorical variable is of interest, a cost-efficient strategy may be to measure the categorical variable only in the tails of the continuous distribution. Such samples occur in population epidemiology and gene mapping. Because central observations are not classified, the mixture component to which each observation belongs is not known. Three cases of censoring, which correspond to differing amounts of available information, are compared. Closed form solutions are not available and so Markov chain Monte Carlo techniques are employed to estimate posterior densities. Evidence for a mixture of two populations is assessed via Bayes factors calculated using a Laplace-Metropolis estimator. Although parameter estimates appear to be satisfactory in most situations, evidence of two populations is only found when the component populations are well separated, tail sizes are not too small, or typing information is available. Extension of these methods to incorporate fixed effects is illustrated by application to a cattle breeding experiment.

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Author notes

  1. Peter Baker (Research Statistician)

    Present address: CSIRO Mathematical and Information Sciences, Queensland Bioscience Precinct, 306 Carmody Road, 4067, ST LUCIA, QLD, Australia

  2. Gerard Davis (Managing Director of Genetic Solutions Pty Ltd)

    Present address: , P. O. Box 145, 4010, Albion, Qld, Australia

Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD, Australia

    Kerrie Mengersen (Research Chair in Statistics)

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  1. Peter Baker
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Correspondence to Peter Baker.

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Baker, P., Mengersen, K. & Davis, G. A bayesian solution to reconstructing centrally censored distributions. JABES 10, 61–83 (2005). https://doi.org/10.1198/108571105X28697

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  • DOI: https://doi.org/10.1198/108571105X28697

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