Sampling, feasibility, and priors in Bayesian estimation

TL;DR

This paper explores importance sampling and implicit sampling in Bayesian data assimilation, analyzing feasibility conditions, convergence of particle filters, and the challenge of selecting appropriate priors, emphasizing the importance of data and physics.

Contribution

It provides a detailed analysis of implicit sampling for efficient data assimilation and introduces new insights into the feasibility conditions and prior selection in Bayesian estimation.

Findings

Feasibility depends on the Frobenius norm of the noise covariance matrix.

Implicit sampling enhances efficiency in particle filters.

Progress reported on determining appropriate priors for data assimilation.

Abstract

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.