Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures
In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to...
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| Format: | Journal article |
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Institute of Mathematical Statistics
2016
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| _version_ | 1826299666886557696 |
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| author | Filippi, S Holmes, C Nieto Barajas, L |
| author_facet | Filippi, S Holmes, C Nieto Barajas, L |
| author_sort | Filippi, S |
| collection | OXFORD |
| description | In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a \null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets. |
| first_indexed | 2024-03-07T05:05:25Z |
| format | Journal article |
| id | oxford-uuid:d9c1b009-e2ff-4217-8be4-ab715fc7cb91 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:05:25Z |
| publishDate | 2016 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:d9c1b009-e2ff-4217-8be4-ab715fc7cb912022-03-27T08:58:12ZScalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process MixturesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d9c1b009-e2ff-4217-8be4-ab715fc7cb91Symplectic Elements at OxfordInstitute of Mathematical Statistics2016Filippi, SHolmes, CNieto Barajas, LIn this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a \null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets. |
| spellingShingle | Filippi, S Holmes, C Nieto Barajas, L Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title | Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title_full | Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title_fullStr | Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title_full_unstemmed | Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title_short | Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures |
| title_sort | scalable bayesian nonparametric measures for exploring pairwise dependence via dirichlet process mixtures |
| work_keys_str_mv | AT filippis scalablebayesiannonparametricmeasuresforexploringpairwisedependenceviadirichletprocessmixtures AT holmesc scalablebayesiannonparametricmeasuresforexploringpairwisedependenceviadirichletprocessmixtures AT nietobarajasl scalablebayesiannonparametricmeasuresforexploringpairwisedependenceviadirichletprocessmixtures |