Bayesian Covariance Estimation for Multi-group Matrix-variate Data
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914706496684032 |
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| author | Bersson, Elizabeth Hoff, Peter D. |
| author_facet | Bersson, Elizabeth Hoff, Peter D. |
| contents | Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation methods which shrink an unstructured, group-specific covariance either across groups towards a pooled covariance or within each group towards a Kronecker structure have been developed. However, in many applications, it is unclear which approach will result in more accurate covariance estimates. In this article, we present a hierarchical prior distribution which flexibly allows for both types of shrinkage. The prior linearly combines shrinkage across groups towards a shared pooled covariance and shrinkage within groups towards a group-specific Kronecker covariance. We illustrate the utility of the proposed prior in speech recognition and an analysis of chemical exposure data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09211 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bayesian Covariance Estimation for Multi-group Matrix-variate Data Bersson, Elizabeth Hoff, Peter D. Methodology Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation methods which shrink an unstructured, group-specific covariance either across groups towards a pooled covariance or within each group towards a Kronecker structure have been developed. However, in many applications, it is unclear which approach will result in more accurate covariance estimates. In this article, we present a hierarchical prior distribution which flexibly allows for both types of shrinkage. The prior linearly combines shrinkage across groups towards a shared pooled covariance and shrinkage within groups towards a group-specific Kronecker covariance. We illustrate the utility of the proposed prior in speech recognition and an analysis of chemical exposure data. |
| title | Bayesian Covariance Estimation for Multi-group Matrix-variate Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2302.09211 |