@article{PathirajaMoradkhaniMarshalletal.2018,
  author    = {Pathiraja, Sahani Darschika and Moradkhani, H. and Marshall, L. and Sharma, Ashish and Geenens, G.},
  title     = {Data-driven model uncertainty estimation in hydrologic data assimilation},
  series = {Water resources research : WRR / American Geophysical Union},
  volume    = {54},
  journal   = {Water resources research : WRR / American Geophysical Union},
  number    = {2},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0043-1397},
  doi       = {10.1002/2018WR022627},
  pages     = {1252 -- 1280},
  year      = {2018},
  abstract  = {The increasing availability of earth observations necessitates mathematical methods to optimally combine such data with hydrologic models. Several algorithms exist for such purposes, under the umbrella of data assimilation (DA). However, DA methods are often applied in a suboptimal fashion for complex real-world problems, due largely to several practical implementation issues. One such issue is error characterization, which is known to be critical for a successful assimilation. Mischaracterized errors lead to suboptimal forecasts, and in the worst case, to degraded estimates even compared to the no assimilation case. Model uncertainty characterization has received little attention relative to other aspects of DA science. Traditional methods rely on subjective, ad hoc tuning factors or parametric distribution assumptions that may not always be applicable. We propose a novel data-driven approach (named SDMU) to model uncertainty characterization for DA studies where (1) the system states are partially observed and (2) minimal prior knowledge of the model error processes is available, except that the errors display state dependence. It includes an approach for estimating the uncertainty in hidden model states, with the end goal of improving predictions of observed variables. The SDMU is therefore suited to DA studies where the observed variables are of primary interest. Its efficacy is demonstrated through a synthetic case study with low-dimensional chaotic dynamics and a real hydrologic experiment for one-day-ahead streamflow forecasting. In both experiments, the proposed method leads to substantial improvements in the hidden states and observed system outputs over a standard method involving perturbation with Gaussian noise.},
  language  = {en}
}
@article{CarpentierKim2018,
  author    = {Carpentier, Alexandra and Kim, Arlene K. H.},
  title     = {An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution},
  series = {Statistica Sinica},
  volume    = {28},
  journal   = {Statistica Sinica},
  number    = {3},
  publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica},
  address   = {Taipei},
  issn      = {1017-0405},
  doi       = {10.5705/ss.202016.0103},
  pages     = {1371 -- 1393},
  year      = {2018},
  abstract  = {We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.},
  language  = {en}
}