Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Onsager--Machlup functional for data assimilation   When taking the model error into account in data assimilation, one needs to
evaluate the prior distribution represented by the Onsager--Machlup functional.
Through numerical experiments, this study clarifies how the prior distribution
should be incorporated into cost functions for discrete-time estimation
problems. Consistent with previous theoretical studies, the divergence of the
drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not nec
essary in Markov chain Monte Carlo with the Euler scheme. Although the former
property may cause difficulties when implementing w4D-Var in large systems,
this paper proposes a new technique for estimating the divergence term and its
derivative.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat