Bayesian Clustering for Distributions

Oregon Convention Center 

Scientists often collect samples on characteristics of different observation units and wonder whether the characteristics of the observation units have similar distributional structure. In this study, we propose a new Bayesian clustering method for distributions that uses a T-EP (Truncated Ewens-Pitman) distribution as the prior for the partitioning parameters, that is, for the number of clusters and the cluster sizes. For a given number of clusters, we consider an entropy-based objective function that is naturally derived from the modified Jensen-Shannon divergence between two distributions. This leads to a hierarchical Bayesian clustering method for distributions.

As a motivational example, we introduce yellowfin tuna fork length data collected from the tuna catch of purse-seine vessels that operated in the eastern Pacific Ocean. The hierarchical Bayesian clustering method, applied to density estimates of yellowfin tuna fork length for 5-degree square areas, was used to explore spatial structure in the length composition of the tuna catch.

Hierarchical Bayesian model

Modified Jensen-Shannon divergence

Clustering for distributions

Truncated Ewens-Pitman distribution

Density estimates 

Section on Statistics and the Environment