Related papers: Bayesian Parameter Estimation via Filtering and Fu…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitating approximate methods. Though widely used, these methods…
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…
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new…
A Kalman filter can be used to determine material parameters using uncertain experimental data. However, starting with inappropriate initial values for material parameters might include false local attractors or even divergence. Also,…
Many systems arising in biological applications are subject to periodic forcing. In these systems the forcing parameter is not only time-varying but also known to have a periodic structure. We present an approach to estimating periodic,…
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…
We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to…
We formulate the discrete-time inverse optimal control problem of inferring unknown parameters in the objective function of an optimal control problem from measurements of optimal states and controls as a nonlinear filtering problem. This…
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when…
In many scientific fields, researchers are interested in discovering features with substantial effect on the response from a large number of features while controlling the proportion of false discoveries. By incorporating the knockoff…
This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of…
We consider the problem of local radioelectric property estimation from global electromagnetic scattering measurements. This challenging ill-posed high dimensional inverse problem can be explored by intensive computations of a parallel…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the…