Related papers: Bayesian Parameter Estimation via Filtering and Fu…

We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…

This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…

Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…

Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…

This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is…

The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…

The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…

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…

This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the…

This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…

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…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…

In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…