Validating uncertainty propagation approaches for two-stage Bayesian spatial models using simulation-based calibration
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908245440856064 |
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| author | Villejo, Stephen Jun Martino, Sara Illian, Janine Ryan, William Lindgren, Finn |
| author_facet | Villejo, Stephen Jun Martino, Sara Illian, Janine Ryan, William Lindgren, Finn |
| contents | This work tackles the problem of uncertainty propagation in two-stage Bayesian models, with a focus on spatial applications. A two-stage modeling framework has the advantage of being more computationally efficient than a fully Bayesian approach when the first-stage model is already complex in itself, and avoids the potential problem of unwanted feedback effects. Two ways of doing two-stage modeling are the crude plug-in method and the posterior sampling method. The former ignores the uncertainty in the first-stage model, while the latter can be computationally expensive. This paper validates the two aforementioned approaches and proposes a new approach to do uncertainty propagation, which we call the $\mathbf{Q}$ uncertainty method, implemented using the Integrated Nested Laplace Approximation (INLA). We validate the different approaches using the simulation-based calibration method, which tests the self-consistency property of Bayesian models. Results show that the crude plug-in method underestimates the true posterior uncertainty in the second-stage model parameters, while the resampling approach and the proposed method are correct. We illustrate the approaches in a real life data application which aims to link relative humidity and Dengue cases in the Philippines for August 2018. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Validating uncertainty propagation approaches for two-stage Bayesian spatial models using simulation-based calibration Villejo, Stephen Jun Martino, Sara Illian, Janine Ryan, William Lindgren, Finn Methodology Computation This work tackles the problem of uncertainty propagation in two-stage Bayesian models, with a focus on spatial applications. A two-stage modeling framework has the advantage of being more computationally efficient than a fully Bayesian approach when the first-stage model is already complex in itself, and avoids the potential problem of unwanted feedback effects. Two ways of doing two-stage modeling are the crude plug-in method and the posterior sampling method. The former ignores the uncertainty in the first-stage model, while the latter can be computationally expensive. This paper validates the two aforementioned approaches and proposes a new approach to do uncertainty propagation, which we call the $\mathbf{Q}$ uncertainty method, implemented using the Integrated Nested Laplace Approximation (INLA). We validate the different approaches using the simulation-based calibration method, which tests the self-consistency property of Bayesian models. Results show that the crude plug-in method underestimates the true posterior uncertainty in the second-stage model parameters, while the resampling approach and the proposed method are correct. We illustrate the approaches in a real life data application which aims to link relative humidity and Dengue cases in the Philippines for August 2018. |
| title | Validating uncertainty propagation approaches for two-stage Bayesian spatial models using simulation-based calibration |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2502.18962 |