Related papers: Affine-Mapping based Variational Ensemble Kalman F…
Data assimilation combines information from models, measurements, and priors to estimate the state of a dynamical system such as the atmosphere. The Ensemble Kalman filter (EnKF) is a family of ensemble-based data assimilation approaches…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…
Traditional tracking-by-detection systems typically employ Kalman filters (KF) for state estimation. However, the KF requires domain-specific design choices and it is ill-suited to handling non-linear motion patterns. To address these…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted…
The Kalman filter is ubiquitous for state space models because of its desirable statistical properties, ease of implementation, and generally good performance. However, it can perform poorly in the presence of outliers, or measurements with…
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…
By attaching auxiliary event times to the chronologically ordered observations, we formulate the Bayesian multiple changepoint problem of discrete-time observations into that of continuous-time ones. A version of forward-filtering…
We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
The particle filter (PF) and the ensemble Kalman filter (EnKF) are widely used for approximate inference in state-space models. From a Bayesian perspective, these algorithms represent the prior by an ensemble of particles and update it to…
Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…
This paper discusses an efficient parallel implementation of the ensemble Kalman filter based on the modified Cholesky decomposition. The proposed implementation starts with decomposing the domain into sub-domains. In each sub-domain a…
It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high frequency adjustment processes in the model dynamics. Various methods have…