Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices
We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1797098666881712128 |
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| author | Talhouk, A Doucet, A Murphy, K |
| author_facet | Talhouk, A Doucet, A Murphy, K |
| author_sort | Talhouk, A |
| collection | OXFORD |
| description | We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials. 2012 American Statistical Association. Institute of Mathematical Statistics, and Interface Foundation of North America. |
| first_indexed | 2024-03-07T05:12:52Z |
| format | Journal article |
| id | oxford-uuid:dc284bf0-3c01-44de-9cd2-e2457c857922 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:12:52Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:dc284bf0-3c01-44de-9cd2-e2457c8579222022-03-27T09:15:47ZEfficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation MatricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dc284bf0-3c01-44de-9cd2-e2457c857922EnglishSymplectic Elements at Oxford2012Talhouk, ADoucet, AMurphy, KWe propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials. 2012 American Statistical Association. Institute of Mathematical Statistics, and Interface Foundation of North America. |
| spellingShingle | Talhouk, A Doucet, A Murphy, K Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title | Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title_full | Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title_fullStr | Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title_full_unstemmed | Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title_short | Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices |
| title_sort | efficient bayesian inference for multivariate probit models with sparse inverse correlation matrices |
| work_keys_str_mv | AT talhouka efficientbayesianinferenceformultivariateprobitmodelswithsparseinversecorrelationmatrices AT douceta efficientbayesianinferenceformultivariateprobitmodelswithsparseinversecorrelationmatrices AT murphyk efficientbayesianinferenceformultivariateprobitmodelswithsparseinversecorrelationmatrices |