Sampling, feasibility, and priors in data assimilation

Importance sampling algorithms are discussed in detail, with an emphasison 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 moreefficient.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 determinationof appropriate priors; a progress report on recent work on thisproblem is given.The analysis highlights the need for acareful attention both to the data and to the physics in data assimilation problems.