Quotation Malsiner-Walli, Gertraud, Frühwirth-Schnatter, Sylvia, Grün, Bettina. 2019. Telescoping mixtures - Learning the number of components and data clusters in Bayesian mixture analysis. Statistics5@Aegina, Aegina, Griechenland, 06.09.-08.09.


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Abstract

Telescoping mixtures are an extension of sparse finite mixtures (Malsiner-Walli, Fruhwirth-Schnatter and Grun, 2016) by assuming that additional to the unknown number of data clusters also the number of mixture components is unknown and has to be estimated. Telescoping mixtures explicitly distinguish between the number of data clusters K+ and components K in the mixture distribution, and purposely allow for more components thandata clusters. By linking the prior on the number of components to the prior on the mixture weights, it is guaranteed that components remain empty as K increases, making the number of clusters in the data, defined through the partition implied by the allocation variables, random apriori. Telescoping mixtures can be seen as an alternative to infinite mixtures models. We present a simple algorithm for posterior MCMC sampling to jointly sample K, the number of components, and K+, the number of data clusters. The algorithm is compared to standard transdimensional algorithm such as the reversible jump Markov chain Monte Carlo (Richardson and Green, 1997) and the Jain-Neal split-merge sampler (Miller and Harrison, 2018).

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Paper presented at an academic conference or symposium
Language English
Title Telescoping mixtures - Learning the number of components and data clusters in Bayesian mixture analysis
Event Statistics5@Aegina
Year 2019
Date 06.09.-08.09.
Country Greece
Location Aegina
URL https://aueb-analytics.wixsite.com/statistics5

Associations

Projects
Shrinking and Regularizing Finite Mixture Models
People
Malsiner-Walli, Gertraud (Details)
Frühwirth-Schnatter, Sylvia (Details)
External
Grün, Bettina (Johannes Kepler Universität Linz, Austria)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1162 Statistics (Details)
5701 Applied statistics (Details)
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