Synthetic likelihood in misspecified models
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913037360824320 |
|---|---|
| author | Frazier, David T. Drovandi, Christopher Nott, David J. |
| author_facet | Frazier, David T. Drovandi, Christopher Nott, David J. |
| contents | Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the Bayesian synthetic likelihood posterior when the assumed model differs from the actual data generating process. We demonstrate that the Bayesian synthetic likelihood posterior can display a wide range of non-standard behaviours depending on the level of model misspecification, including multimodality and asymptotic non-Gaussianity. Our results suggest that likelihood tempering, a common approach for robust Bayesian inference, fails for synthetic likelihood whilst recently proposed robust synthetic likelihood approaches can ameliorate this behavior and deliver reliable posterior inference under model misspecification. All results are illustrated using a simple running example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03436 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Synthetic likelihood in misspecified models Frazier, David T. Drovandi, Christopher Nott, David J. Statistics Theory Methodology Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the Bayesian synthetic likelihood posterior when the assumed model differs from the actual data generating process. We demonstrate that the Bayesian synthetic likelihood posterior can display a wide range of non-standard behaviours depending on the level of model misspecification, including multimodality and asymptotic non-Gaussianity. Our results suggest that likelihood tempering, a common approach for robust Bayesian inference, fails for synthetic likelihood whilst recently proposed robust synthetic likelihood approaches can ameliorate this behavior and deliver reliable posterior inference under model misspecification. All results are illustrated using a simple running example. |
| title | Synthetic likelihood in misspecified models |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2104.03436 |