Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913610353082368 |
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| author | Wu, Bingjie Jia, Chen |
| author_facet | Wu, Bingjie Jia, Chen |
| contents | Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on an infinitely long coarse-grained trajectory, we obtain a set of sufficient statistics which extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we set up a theoretical framework of parameter inference and nonequilibrium identification for a general Markovian system with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can identify whether the sufficient statistics are enough for empirical estimation of all unknown parameters and we can also provide a quantitative criterion that reveals nonequilibrium. Our nonequilibrium criterion generalizes the one obtained [J. Chem. Phys. 132:041102 (2010)] for a three-state system with two coarse-grained clusters, and is capable of detecting a larger nonequilibrium region compared to the classical criterion based on autocorrelation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations Wu, Bingjie Jia, Chen Statistical Mechanics Mathematical Physics Data Analysis, Statistics and Probability Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on an infinitely long coarse-grained trajectory, we obtain a set of sufficient statistics which extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we set up a theoretical framework of parameter inference and nonequilibrium identification for a general Markovian system with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can identify whether the sufficient statistics are enough for empirical estimation of all unknown parameters and we can also provide a quantitative criterion that reveals nonequilibrium. Our nonequilibrium criterion generalizes the one obtained [J. Chem. Phys. 132:041102 (2010)] for a three-state system with two coarse-grained clusters, and is capable of detecting a larger nonequilibrium region compared to the classical criterion based on autocorrelation functions. |
| title | Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations |
| topic | Statistical Mechanics Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2406.19586 |