Posterior contraction rates of computational methods for Bayesian data assimilation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908410842185728 |
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| author | Burman, Erik Lu, Mingfei |
| author_facet | Burman, Erik Lu, Mingfei |
| contents | In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite element discretization (usually non-conforming). The analysis is based on the coupling of asymptotics between the number of samples and the dimension of discrete spaces. In the finite element discretization, tailor-made discrete priors, instead of the discretization of continuous priors, are used to generate an optimal convergence rate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Posterior contraction rates of computational methods for Bayesian data assimilation Burman, Erik Lu, Mingfei Numerical Analysis Probability Statistics Theory 65N21, 62F15, 35R30, 65N30, 65C60, 35R25 In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite element discretization (usually non-conforming). The analysis is based on the coupling of asymptotics between the number of samples and the dimension of discrete spaces. In the finite element discretization, tailor-made discrete priors, instead of the discretization of continuous priors, are used to generate an optimal convergence rate. |
| title | Posterior contraction rates of computational methods for Bayesian data assimilation |
| topic | Numerical Analysis Probability Statistics Theory 65N21, 62F15, 35R30, 65N30, 65C60, 35R25 |
| url | https://arxiv.org/abs/2506.14685 |