Continuous-discrete smoothing of diffusions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866914930066718720 |
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| author | Mider, Marcin Schauer, Moritz van der Meulen, Frank |
| author_facet | Mider, Marcin Schauer, Moritz van der Meulen, Frank |
| contents | Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in Schauer et al. (2017). We illustrate its efficiency in a number of challenging problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_03807 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Continuous-discrete smoothing of diffusions Mider, Marcin Schauer, Moritz van der Meulen, Frank Computation 60J60, 65C05 (Primary), 62F15 (Secondary) Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in Schauer et al. (2017). We illustrate its efficiency in a number of challenging problems. |
| title | Continuous-discrete smoothing of diffusions |
| topic | Computation 60J60, 65C05 (Primary), 62F15 (Secondary) |
| url | https://arxiv.org/abs/1712.03807 |