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Bayesian Cluster Analysis: Point Estimation and Credible Balls (with Discussion)

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https://projecteuclid.org/euclid.ba/1508378464#abstract
Original languageEnglish
Pages (from-to)559-626
Number of pages68
JournalBayesian analysis
Volume13
Issue number2
Early online date19 Oct 2017
DOIs
Publication statusPublished - Jun 2018

Abstract

Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to popular algorithms such as agglomerative
hierarchical clustering or k-means which return a single clustering solution, Bayesian nonparametric models provide a posterior over the entire space of partitions, allowing one to assess statistical properties, such as uncertainty on
the number of clusters. However, an important problem is how to summarize the
posterior; the huge dimension of partition space and difficulties in visualizing it add to this problem. In a Bayesian analysis, the posterior of a real-valued parameter of interest is often summarized by reporting a point estimate such as the posterior mean along with 95% credible intervals to characterize uncertainty. In this paper, we extend these ideas to develop appropriate point estimates and credible sets to summarize the posterior of the clustering structure based on decision and information theoretic techniques.

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