Expectation-propagation for Bayesian empirical likelihood inference
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912668540993536 |
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| author | Ng, Kenyon Yu, Weichang Bondell, Howard D. |
| author_facet | Ng, Kenyon Yu, Weichang Bondell, Howard D. |
| contents | Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical likelihood offers a semi-parametric alternative by replacing the parametric likelihood with a profile empirical likelihood defined through moment constraints, thereby avoiding explicit distributional assumptions. Despite these advantages, Bayesian empirical likelihood faces substantial computational challenges, including the need to solve a constrained optimization problem for each likelihood evaluation and difficulties with non-convex posterior support, particularly in small-sample settings. This paper introduces a variational approach based on expectation-propagation to approximate the Bayesian empirical-likelihood posterior, balancing computational cost and accuracy without altering the target posterior via adjustments such as pseudo-observations. Empirically, we show that our approach can achieve a superior cost-accuracy trade-off relative to existing methods, including Hamiltonian Monte Carlo and variational Bayes. Theoretically, we show that the approximation and the Bayesian empirical-likelihood posterior are asymptotically equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21174 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expectation-propagation for Bayesian empirical likelihood inference Ng, Kenyon Yu, Weichang Bondell, Howard D. Methodology Computation 62F99 Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical likelihood offers a semi-parametric alternative by replacing the parametric likelihood with a profile empirical likelihood defined through moment constraints, thereby avoiding explicit distributional assumptions. Despite these advantages, Bayesian empirical likelihood faces substantial computational challenges, including the need to solve a constrained optimization problem for each likelihood evaluation and difficulties with non-convex posterior support, particularly in small-sample settings. This paper introduces a variational approach based on expectation-propagation to approximate the Bayesian empirical-likelihood posterior, balancing computational cost and accuracy without altering the target posterior via adjustments such as pseudo-observations. Empirically, we show that our approach can achieve a superior cost-accuracy trade-off relative to existing methods, including Hamiltonian Monte Carlo and variational Bayes. Theoretically, we show that the approximation and the Bayesian empirical-likelihood posterior are asymptotically equivalent. |
| title | Expectation-propagation for Bayesian empirical likelihood inference |
| topic | Methodology Computation 62F99 |
| url | https://arxiv.org/abs/2510.21174 |