A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data

Denti, Francesco; Camerlenghi, Federico; Guindani, Michele; Mira, Antonietta

doi:10.1080/01621459.2021.1933499

Cited by 11 publications

(14 citation statements)

References 35 publications

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Section: Bayesian Nonparametric Priors For Clusteringmentioning

confidence: 98%

“…This feature is not suited to several applications and the discussion to Camerlenghi et al (2019a) provides interesting examples. See also Beraha et al (2021), Christensen & Ma (2020), Denti et al (2021), Soriano & Ma (2019) for further stimulating contributions to this literature. Hence, within the composition structure framework (2), our goal is to obtain a prior distribution able to infer the clustering structure of both populations and observations, which is highly flexible and implementable for a large number of populations and associated samples.…”

Section: Nested Dirichlet Processmentioning

confidence: 99%

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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: Bayesian Nonparametric Priors For Clusteringmentioning

confidence: 98%

Section: Nested Dirichlet Processmentioning

confidence: 99%

Flexible clustering via hidden hierarchical Dirichlet priors

Lijoi

Prünster

Giovanni

2022

Scandinavian J Statistics

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“…However, the massive growth in data acquisition and technologies has led to a number of interesting extensions. This includes combining multiple data sources through data integration [18][19][20], hierarchical Bayesian frameworks for partially exchangeable or nested data [21][22][23][24][25][26][27][28], hidden Markov models and other extensions for temporal data [29,30], accounting for spatially indexed data [31][32][33], incorporating general covariate information [34][35][36][37] and more.…”

Section: Bayesian Cluster Analysismentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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Bayesian cluster analysis offers substantial benefits over algorithmic approaches by providing not only point estimates but also uncertainty in the clustering structure and patterns within each cluster. An overview of Bayesian cluster analysis is provided, including both model-based and loss-based approaches, along with a discussion on the importance of the kernel or loss selected and prior specification. Advantages are demonstrated in an application to cluster cells and discover latent cell types in single-cell RNA sequencing data to study embryonic cellular development. Lastly, we focus on the ongoing debate between finite and infinite mixtures in a model-based approach and robustness to model misspecification. While much of the debate and asymptotic theory focuses on the marginal posterior of the number of clusters, we empirically show that quite a different behaviour is obtained when estimating the full clustering structure. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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“…The atoms ζ⋆ are shared (more precisely, the subset of those atoms that are allocated under c1i are shared). Such ‘common atoms’ BNP mixture models have been shown to be useful in other applications too [25,26].…”

Section: A Common-atoms Bnp Mixture Model For Using Rwdmentioning

confidence: 99%

“…The model is illustrated in figure 2. Similar common-atoms mixture models, without the constraint on the second mixture model to only use the atoms ζk⋆ sampled in the first mixture, are used, for example, in [25]. The latter constraint makes the mixture F0 dependent on the latent ζ⋆, which are therefore introduced in the first line of (3.4).…”

Section: A Common-atoms Bnp Mixture Model For Using Rwdmentioning

confidence: 99%

Bayesian approaches to include real-world data in clinical studies

Müller

Chandra

Sarkar

2023

Phil. Trans. R. Soc. A.

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Randomized clinical trials have been the mainstay of clinical research, but are prohibitively expensive and subject to increasingly difficult patient recruitment. Recently, there is a movement to use real-world data (RWD) from electronic health records, patient registries, claims data and other sources in lieu of or supplementing controlled clinical trials. This process of combining information from diverse sources calls for inference under a Bayesian paradigm. We review some of the currently used methods and a novel non-parametric Bayesian (BNP) method. Carrying out the desired adjustment for differences in patient populations is naturally done with BNP priors that facilitate understanding of and adjustment for population heterogeneities across different data sources. We discuss the particular problem of using RWD to create a synthetic control arm to supplement single-arm treatment only studies. At the core of the proposed approach is the model-based adjustment to achieve equivalent patient populations in the current study and the (adjusted) RWD. This is implemented using common atoms mixture models. The structure of such models greatly simplifies inference. The adjustment for differences in the populations can be reduced to ratios of weights in such mixtures. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data

Cited by 11 publications

References 35 publications

Flexible clustering via hidden hierarchical Dirichlet priors

Flexible clustering via hidden hierarchical Dirichlet priors

Bayesian cluster analysis

Bayesian approaches to include real-world data in clinical studies

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