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Sampling, feasibility, and priors in Bayesian estimation Public Deposited

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  • Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors; a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.
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  • Chorin, A. J., Lu, F., Miller, R. N., Morzfeld, M., & Tu, X. (2015). Sampling, feasibility, and priors in Bayesian estimation. Discrete and Continuous Dynamical Systems - Series A, 36(8), 4227-4246. doi:10.3934/dcds.2016.8.4227
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  • This work was supported in part by the Director, Office of Science, Computational and Technology Research, U.S. Department of Energy, under Contract No. DE-AC02-05CH11231, and by the National Science Foundation under grants DMS-1217065, DMS-1419044, DMS1115759 and DMS1419069.
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