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Wiley Interdisciplinary Reviews:
WIREs Computational Statistics
Volume 13 Issue 4 (July 2021)
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Why BDeu? Regular Bayesian network structure learning with discrete and continuous variables
Published Online: Mar 01 2021
DOI: 10.1002/wics.1554
We consider the problem of Bayesian network structure learning (BNSL) from data. In particular, we focus on the score‐based approach rather than the constraint‐based one and address what score we should use for the purpose. The Bayesian Dirichlet equivalent uniform (BDeu) has been mainly used in the community of BNs (not outside it). We know that for any model selection and any data, the fitter the data to a model, the complex the model, and vice versa. However, recently, it was proved that the BDeu violates the regularity, which means that it does not balance the two factors, although it works satisfactorily (consistency) when the sample size is infinitely large. Besides, we claim that the merit of using the regular scores over the BDeu is that tighter bounds of pruning rules are available when we consider efficient BNSL. Finally, we compare by the experiments the performances of the procedures to examine the claim. (This paper is for review and gives a unified viewpoint from the recent progress on the topic.).
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Bayesian mixture models for cytometry data analysis
Published Online: Oct 16 2020
DOI: 10.1002/wics.1535
Blood samples are drawn from each subjects. Every sample is then split into two aliquots: one to stimulate with antigen and the other is left unstimulated as a negative control. After stimulation, whole peripheral blood mononuclear cells are labeled with fluorophore‐conjugated antibodies against phenotypic and functional markers. The expression of each marker on each cell is measured by flow cytometry. After acquisition, data are processed and statistical mixture models can be used to identify distinct cell populations. Once the cell subsets are given, the statistical mixture models can also be applied for further diagnosis and discovery, such as detecting differentially expressed cell subsets between condition (stimulation vs. unstimulation), and relating cell subsets to external variables (e.g., subjects’ outcome).
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Robust linear regression for high‐dimensional data: An overview
Published Online: Jul 08 2020
DOI: 10.1002/wics.1524
The big data era increases the probability of data outliers, and this leads to an urgent need of robust statistical methods, as described here for the high‐dimensional regression problem.
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A review of Bayesian group selection approaches for linear regression models
Published Online: Jun 29 2020
DOI: 10.1002/wics.1513
Grouping selection arises naturally in many statistical modeling problems. Here we review the Bayesian group selection approaches for linear regression models. We start from the Bayesian indicator approach and then move to the Bayesian group LASSO methods. In addition, we mention some extensions of Bayesian group selection for the generalized linear models and the multiple response models.
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Focus Article

A convergence diagnostic for Bayesian clustering
Published Online: Nov 10 2020
DOI: 10.1002/wics.1536
Metabolite measurements plots with agglomerative spike‐and‐slab Bayesian clustering dendrogram. We explore the convergence of the Gibbs sampler and split‐merge sampler on the same model.
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