Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 15, Issue 2, Pages 4295-4342Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/21-EJS1894
Keywords
Chemical reaction network; data assimilation; diffusion bridge; filtering; guided proposal; Lorenz system; Markov Chain Monte Carlo; partial observations; stochastic heat equation on a graph
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Funding
- European Research Council [320637]
- Max Planck Institute for Mathematics in the Sciences, Leipzig
- EPSRC [EP/L016710/1]
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This study introduces a novel algorithm for sampling from the exact smoothing distribution and applies it to parameter estimation. The algorithm is called the BFFG algorithm. The method demonstrates efficiency in addressing several challenging problems.
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 [53]. We illustrate its efficiency in a number of challenging problems.
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