Related papers: Evaluating Data Assimilation Algorithms
The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
Data assimilation will be essential for the management and expansion of geological carbon storage operations. In traditional data assimilation approaches a fixed set of geological hyperparameters, such as mean and standard deviation of…
Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…
Bayesian interpretations of neural processing require that biological mechanisms represent and operate upon probability distributions in accordance with Bayes' theorem. Many have speculated that synaptic failure constitutes a mechanism of…
We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the…
This paper introduces the {\it particle swarm filter} (not to be confused with particle swarm optimization): a recursive and embarrassingly parallel algorithm that targets an approximation to the sequence of posterior predictive…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. The weights given to the observations and background state depend on their specified error…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…
Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…
We study a discrete-in-time data-assimilation algorithm based on nudging through a time-delayed feedback control in which the observational measurements have been contaminated by a Gaussian noise process. In the context of the…
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems,…