Importance conditional sampling for Pitman-Yor mixtures

Canale, Antonio; Corradin, Riccardo; Nipoti, Bernardo

doi:10.48550/arxiv.1906.08147

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Therefore, we specify a model allowing to capture differences between the centers since different groups of hospitals can serve different women. Canale et al (2019) provide further analysis of the CPP data.…”

Section: Cpp Datamentioning

confidence: 99%

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: Cpp Datamentioning

confidence: 99%

Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi

Prünster

Giovanni

2022

Scandinavian J Statistics

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“…In case (iii), the whole set of parameters cannot be physically stored in a computer, and algorithms need to rely on marginalization techniques (see, e.g. Neal 2000;Walker 2007;Papaspiliopoulos and Roberts 2008;Kalli, Griffin, and Walker 2011;Griffin and Walker 2011;Canale et al 2021). Case (ii) requires a transdimensional MCMC sampler (Green 1995), examples of which are the split-merge reversible jump MCMC (Richardson and Green 1997) and the birth-death Metropolis-Hastings (Stephens 2000) algorithm.…”

Section: Bayesian Mixture Modelsmentioning

confidence: 99%

BayesMix: Bayesian Mixture Models in C++

Beraha¹,

Bruno²,

Gianella³

et al. 2022

Preprint

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We describe BayesMix, a C++ library for MCMC posterior simulation for general Bayesian mixture models. The goal of BayesMix is to provide a self-contained ecosystem to perform inference for mixture models to computer scientists, statisticians and practitioners. The key idea of this library is extensibility, as we wish the users to easily adapt our software to their specific Bayesian mixture models. In addition to the several models and MCMC algorithms for posterior inference included in the library, new users with little familiarity on mixture models and the related MCMC algorithms can extend our library with minimal coding effort. Our library is computationally very efficient when compared to competitor software. Examples show that the typical code runtimes are from two to 25 times faster than competitors for data dimension from one to ten. Our library is publicly available on Github at https://github.com/bayesmix-dev/bayesmix/.

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Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi,

Prünster,

Rebaudo

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Importance conditional sampling for Pitman-Yor mixtures

Cited by 3 publications

References 28 publications

Flexible clustering via hidden hierarchical Dirichlet priors

Flexible clustering via hidden hierarchical Dirichlet priors

BayesMix: Bayesian Mixture Models in C++

Flexible clustering via hidden hierarchical Dirichlet priors

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