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This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont. Here we describe some of the circumstances under which statistical ecologists might…
Filters, especially wide range of Kalman Filters have shown their impacts on predicting variables of stochastic models with higher accuracy then traditional statistic methods. Updating mean and covariance each time makes Bayesian inferences…
Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
State estimation in power distribution systems is a key component for increased reliability and optimal system performance. Well understood in transmission systems, state estimation is now an area of active research in distribution…
We consider the solution of inverse problems in dynamic contrast-enhanced imaging by means of Ensemble Kalman Filters. Our quantity of interest is blood perfusion, i.e. blood flow rates in tissue. While existing approaches to compute blood…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…
The parameters of temporal models, such as dynamic Bayesian networks, may be modelled in a Bayesian context as static or atemporal variables that influence transition probabilities at every time step. Particle filters fail for models that…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable…
The Kalman Filter has been called one of the greatest inventions in statistics during the 20th century. Its purpose is to measure the state of a system by processing the noisy data received from different electronic sensors. In comparison,…
Since the groundbreaking work of the Kalman filter in the 1960s, considerable effort has been devoted to various discrete time filters for dynamic state estimation, especially including dozens of different types of suboptimal…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…
The unscented Kalman filter is a nonlinear estimation algorithm commonly used in navigation applications. The prediction of the mean and covariance matrix is crucial to the stable behavior of the filter. This prediction is done by…