A Practical Implementation of the Gibbs Sampler for Mixture of Distributions: Application to the Determination of Specifications in Food Industry

Julien Cornebise (1) , Myriam Maumy (2) , Philippe Girard (3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 IRMA - Institut de Recherche Mathématique Avancée
3 QMD - Quality Management Department

This article, mainly targeted to practitioners, illustrates practical issues that may arise when applying MCMC technics to a mixture of distributions model on real data. This data is provided by coffee manufacturer to determine specifications for soluble coffee. Assuming a known number of components, parameters of each component are estimated using the Gibbs sampler and specifications are derived as the 99% quantile of the first distribution. Convergence and label-switching are discussed. Determination of the number of components is also considered, via model selection using the Bayes Factors.

Domaines: Statistiques [math.ST]

Julien Cornebise, Myriam Maumy, Philippe Girard. A Practical Implementation of the Gibbs Sampler for Mixture of Distributions: Application to the Determination of Specifications in Food Industry. 2005, pp.828-838. ⟨hal-00141710⟩