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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00538 |
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| _version_ | 1866909838513012736 |
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| author | Hamura, Yasuyuki |
| author_facet | Hamura, Yasuyuki |
| contents | We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global prior under some assumptions, we prove geometric ergodicity for a Gibbs algorithm in which it is relatively easy to update the global shrinkage parameter. Second, we consider a more general class of global-local shrinkage priors. Under milder conditions, geometric ergodicity is proved for two- and three-stage Gibbs samplers based on rejection sampling. We also construct a practical rejection sampling method in the horseshoe case. Finally, a simulation study is performed to compare proposed and existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Ergodicity of Gibbs Algorithms for a Normal Model With a Global-Local Shrinkage Prior Hamura, Yasuyuki Statistics Theory Computation We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global prior under some assumptions, we prove geometric ergodicity for a Gibbs algorithm in which it is relatively easy to update the global shrinkage parameter. Second, we consider a more general class of global-local shrinkage priors. Under milder conditions, geometric ergodicity is proved for two- and three-stage Gibbs samplers based on rejection sampling. We also construct a practical rejection sampling method in the horseshoe case. Finally, a simulation study is performed to compare proposed and existing methods. |
| title | Geometric Ergodicity of Gibbs Algorithms for a Normal Model With a Global-Local Shrinkage Prior |
| topic | Statistics Theory Computation |
| url | https://arxiv.org/abs/2503.00538 |