Author: M. WestPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Aspects of Recursive Bayesian Estimation
Recursive Bayesian Estimation of Time Intervals
Author: Yang, XiPublisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 78
Book Description
Bayesian Filtering and Smoothing
Author: Simo SärkkäPublisher: Cambridge University Press
ISBN: 110703065X
Category : Computers
Languages : en
Pages : 255
Book Description
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
The Bayesian Approach to Recursive State Estimation
Author: Stuart Charles KramerPublisher:
ISBN:
Category : Bayesian statistical decision theory
Languages : en
Pages : 268
Book Description
In Bayesian estimation, the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity. This work considers recursive estimation of a nonlinear discrete-time system state using successive observations. The formal recursion for the density function is easily written, but generally there is no closed form solution. The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions. The critical part of the algorithm then becomes a discrete linear convolution that can be realized using FFT's. Keywords: error analysis; and parameter estimation.
Algorithms and Programs of Dynamic Mixture Estimation
Author: Ivan NagyPublisher: Springer
ISBN: 3319646710
Category : Mathematics
Languages : en
Pages : 118
Book Description
This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.
Recursive Bayesian Estimation
Author: Niclas BergmanPublisher:
ISBN: 9789172194731
Category : Bayesian statistical decision theory
Languages : en
Pages : 204
Book Description
Recursive Bayesian Methods for Sequential Parameter-state Estimation
Author: Yinan HuangPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
A central theme in applied and computational statistics is the accurate and efficient methods of inference. The Bayesian paradigm performs inference based on the posterior distribution of unknown quantities. Throughout decades, there has been an enormous literature on computational Bayesian methods. Practical implementations, while succussful to different degrees, usually impose certain restrictions on the specific model structure. As more applications rely on complex model dynamics, more challenges remain to tackle the curse of high dimensionality and the analytical intractability of many non-Gaussian distributions. This thesis builds on existing research in the field of sequential Bayesian estimation for a general class of state-space models. We establish recursive Bayesian simulation algorithms to estimate parameters and states for a variety of diffusion and jump stochastic models. Our main work and contribution are two-fold. First, we build a particle filter framework for Levy-type state-space models. Particle filters are efficient numerical simulation techniques ideally suitable for highly nonlinear models, with a significant computational advantage over the standard Markov Chain Monte Carlo. Our particle filters can effectively estimate parameters and state variables for non-Gaussian dynamics. We perform empirical testing on financial time series, and find that certain Levy-type small jump processes can be a substitute of the usual Brownian motion-based random walk models. In addition, we propose a general Variational Bayes Particle Filter framework. It is applicable to a wider class of models with a large number of dimensions. Secondly, we build a Variational Bayes estimator for Hidden Markov Models with observational jumps. This is a typical setup for numerous biostatistical data analysis, where huge amounts of streaming data need to be sequentially filtered for potential evidence of the existence of quantitative traits or genetic features. Our algorithm works to identify and classify different responses. The hidden Markov estimator is robust and highly adaptable. In addition, this thesis also includes a self-contained chapter on the technique of Markovian projection. It reduces a complicated multi-dimensional dynamics to a one-dimensional simple Markovian process with identical marginal distributions, therefore keeping certain path-independent expectation values invariant. The projection has certain implications in the pricing of European-style options in financial mathematics. We provide a theorem generalizing existing results to the general Levy jump models, and discuss calibration issues.
Causual Modelling Using Recursive Bayesian Estimation and Kalman Filtering on Data of Variable Precision
Author: A. SolomonStochastic Processes and Filtering Theory
Author: Andrew H. JazwinskiPublisher: Courier Corporation
ISBN: 0486318192
Category : Science
Languages : en
Pages : 404
Book Description
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.
Author: Kailai Li