Clustering Areal Units at Multiple Levels of Resolution to Model Crime in Philadelphia

Balocchi, Cecilia; George, Edward I.; Jensen, Shane T.

doi:10.48550/arxiv.2112.02059

Cited by 2 publications

(1 citation statement)

References 46 publications

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“…Hence, as a by-product, our theoretical results shed also some light on the topic modeling applications of Agrawal et al (2013). Additionally, the same model was independently applied in Balocchi et al (2021) to successfully cluster urban areal units at different levels of resolution simultaneously.…”

Section: Introductionmentioning

confidence: 69%

Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi

Prünster

Giovanni

2022

Scandinavian J Statistics

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The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering method for both samples and observations, we investigate a nonparametric prior that arises as the composition of two different discrete random structures and derive a closed-form expression for the induced distribution of the random partition, the fundamental tool regulating the clustering behavior of the model. On the one hand, this allows to gain a deeper insight into the theoretical properties of the model and, on the other hand, it yields an MCMC algorithm for evaluating Bayesian inferences of interest. Moreover, we single out limitations of this algorithm when working with more than two populations and, consequently, devise an alternative more efficient sampling scheme, which as a by-product, allows testing homogeneity between different populations. Finally, we perform a comparison with the nestedThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Introductionmentioning

confidence: 69%

Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi

Prünster

Giovanni

2022

Scandinavian J Statistics

View full text Add to dashboard Cite

show abstract

Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi,

Prünster,

Rebaudo

2022

Preprint

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The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering method for both samples and observations, we investigate a nonparametric prior that arises as the composition of two different discrete random structures and derive a closed-form expression for the induced distribution of the random partition, the fundamental tool regulating the clustering behavior of the model. On the one hand, this allows to gain a deeper insight into the theoretical properties of the model and, on the other hand, it yields an MCMC algorithm for evaluating Bayesian inferences of interest. Moreover, we single out limitations of this algorithm when working with more than two populations and, consequently, devise an alternative more efficient sampling scheme, which as a by-product, allows testing homogeneity between different populations. Finally, we perform a comparison with the nested Dirichlet process and provide illustrative examples of both synthetic and real data.

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Clustering Areal Units at Multiple Levels of Resolution to Model Crime in Philadelphia

Cited by 2 publications

References 46 publications

Flexible clustering via hidden hierarchical Dirichlet priors

Flexible clustering via hidden hierarchical Dirichlet priors

Flexible clustering via hidden hierarchical Dirichlet priors

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