Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous accuracy and robustness analysis for two-scale reduced random
  Kalman filters in high dimensions   Contemporary data assimilation often involves millions of prediction
variables. The classical Kalman filter is no longer computationally feasible in
such a high dimensional context. This problem can often be resolved by
exploiting the underlying multiscale structure, applying the full Kalman
filtering procedures only to the large scale vari- ables, and estimating the
small scale variables with proper statistical strategies, including
multiplicative inflation, representation model error in the observations, and
crude localization. The resulting two-scale reduced filters can have close to
optimal numerical filtering skill based on previous numerical evidence. Yet, no
rigorous explanation exists for this success, because these modifications
create unavoidable bias and model error. This paper contributes to this issue
by establishing a new error analysis framework for two different reduced random
Kalman filters, valid independent of the large dimension. The first part of our
results examines the fidelity of the covariance estimators, which is essential
for accurate uncertainty quantification. In a simplified setting, this is
demonstrated by showing the true error covariance is dominated by its
estimators. In general settings, the Mahalanobis error and its intrinsic
dissipation can indicate covariance fidelity. The second part develops upper
bounds for the covariance estimators by comparing with proper Kalman filters.
Combining both results, the classical tools for Kalman filters can be used as
a-priori performance criteria for the reduced filters. In applications, these
criteria guarantee the reduced filters are robust, and accurate for small noise
systems. They also shed light on how to tune the reduced filters for stochastic
turbulence.

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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn