Scalable simulation-based inference for implicitly defined models using a metamodel for Monte Carlo log-likelihood estimator
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909580672368640 |
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| author | Park, Joonha |
| author_facet | Park, Joonha |
| contents | Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate Bayesian computation (ABC), often scale poorly as data size increases. We develop a scalable inference method for implicitly defined models using a metamodel for the Monte Carlo log-likelihood estimator derived from simulations. This metamodel characterizes both statistical and simulation-based randomness in the distribution of the log-likelihood estimator across different parameter values. Our metamodel-based method quantifies uncertainty in parameter estimation in a principled manner, leveraging the local asymptotic normality of the mean function of the log-likelihood estimator. We apply this method to construct accurate confidence intervals for parameters of partially observed Markov process models where the Monte Carlo log-likelihood estimator is obtained using the bootstrap particle filter. We numerically demonstrate that our method enables accurate and highly scalable parameter inference across several examples, including a mechanistic compartment model for infectious diseases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scalable simulation-based inference for implicitly defined models using a metamodel for Monte Carlo log-likelihood estimator Park, Joonha Methodology Statistics Theory 62E20, 62F03, 62F25, 62M02 Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate Bayesian computation (ABC), often scale poorly as data size increases. We develop a scalable inference method for implicitly defined models using a metamodel for the Monte Carlo log-likelihood estimator derived from simulations. This metamodel characterizes both statistical and simulation-based randomness in the distribution of the log-likelihood estimator across different parameter values. Our metamodel-based method quantifies uncertainty in parameter estimation in a principled manner, leveraging the local asymptotic normality of the mean function of the log-likelihood estimator. We apply this method to construct accurate confidence intervals for parameters of partially observed Markov process models where the Monte Carlo log-likelihood estimator is obtained using the bootstrap particle filter. We numerically demonstrate that our method enables accurate and highly scalable parameter inference across several examples, including a mechanistic compartment model for infectious diseases. |
| title | Scalable simulation-based inference for implicitly defined models using a metamodel for Monte Carlo log-likelihood estimator |
| topic | Methodology Statistics Theory 62E20, 62F03, 62F25, 62M02 |
| url | https://arxiv.org/abs/2311.09446 |