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THE RESTRICTED VARIATIONAL BAYES APPROXIMATION IN BAYESIAN FILTERING
"... The Variational Bayes (VB) approach is used as a onestep approximation for Bayesian filtering. It requires the availability of moments of the freeform distributional optimizers. The latter may have intractable functional forms. In this contribution, we replace these by appropriate fixedform distr ..."
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The Variational Bayes (VB) approach is used as a onestep approximation for Bayesian filtering. It requires the availability of moments of the freeform distributional optimizers. The latter may have intractable functional forms. In this contribution, we replace these by appropriate fixedform distributions yielding the required moments. We address two scenarios of this Restricted VB (RVB) approximation. For the first scenario, an application in identification of HMMs is given. In the second, the fixedform distribution is generated via Particle Filtering (PF). It is shown that a new approximation of RaoBlackwellized particle filtering is obtained in this scenario of RVB. Its performance is assessed for a simple nonlinear model. 1. THE VB APPROXIMATION The VB approximation is a deterministic freeform optimization technique. It was first used in offline inference problems [1] and extended to online inference of timeinvariant parameters in [2]. The use of VB in Bayesian filtering was first discussed in [3]. The key theory is now reviewed. Theorem 1 (Variational Bayes (VB)) Let f (θD) be the posterior distribution of multivariate parameter, θ = [θ ′ 1, θ ′ 2] ′, and ˘ f (θD) be an approximate distribution restricted to the set of conditionally independent distributions ˘f (θD) = ˘ f (θ1, θ2D) = ˘ f (θ1D) ˘ f (θ2D). (1) The minimum of the KullbackLeibler divergence ˜f (θD) = arg min KL ˘f (θD) f (θD) , (2)
Generated using version 3.0 of the official AMS LATEX template Marginalized Particle Filtering Framework for Tuning of Ensemble Filters
, 2010
"... Marginalized particle filtering (MPF), also known as RaoBlackwellized particle filtering, has been recently developed as a hybrid method combining analytical filters with particle filters. In this paper, we investigate the prospects of this approach in enviromental modelling where the key concerns ..."
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Marginalized particle filtering (MPF), also known as RaoBlackwellized particle filtering, has been recently developed as a hybrid method combining analytical filters with particle filters. In this paper, we investigate the prospects of this approach in enviromental modelling where the key concerns are nonlinearity, highdimensionality, and computational cost. In our formulation, exact marginalization in the MPF is replaced by approximate marginalization yielding a framework for creation of new hybrid filters. In particular, we propose to use the MPF framework for online tuning of nuisance parameters of ensemble filters. Conditional independence based simplification of the MPF algorithm is proposed for computational reasons and its close relation to previously published methods is discussed. Strength of the framework is demonstrated on the joint estimation of the inflation factor, the measurement error variance and the lengthscale parameter of covariance localization. It is shown that accurate estimation can be achieved with a moderate number of particles. Moreover, this result was achieved with naively chosen proposal densities leaving space for further improvements. 1.