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Paper No. 10-20

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FJ Rubio and MFJ Steel

Inference for grouped data with a truncated skew-Laplace distribution

Abstract: The skew-Laplace distribution has been used for modelling particle size with point observations. In reality, the observations are truncated and grouped (rounded). This must be formally taken into account for accurate modelling, and it is shown how this leads to convenient closed-form expressions for the likelihood in this model. In a Bayesian framework, we specify “noninformative” benchmark priors which only require the choice of a single scalar prior hyperparameter. We derive conditions for the existence of the posterior distribution when rounding and various forms of truncation are considered in the model. We will focus mostly on modelling microbiological data obtained with flow cytometry using a skew-Laplace distribution. However, we also use the model on data often used to illustrate other skewed distributions, and we show that our modelling favourably compares with the popular and flexible skew-Student models. Further examples on simulated data illustrate the wide applicability of the model.

Keywords: Bayesian inference; flow cytometry data; glass fibre data; posterior existence; rounding.