Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

Caron, François; Davy, Manuel; Doucet, Arnaud; Duflos, Emmanuel; Vanheeghe, Philippe

doi:10.1109/tsp.2007.900167

Cited by 94 publications

(66 citation statements)

References 44 publications

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“…Liu et al (1999) and Fearnhead (2003)). Recently, Caron et al (2006) have developed methods for state space models where the noise in the observation equation and the system equation is assumed to arise from an unknown distribution given a Dirichlet process prior, which is time-invariant. In this paper, we propose an algorithm based on the work of Fearnhead (2003) and Caron et al (2006).…”

Section: Particle Filtersmentioning

confidence: 99%

“…In previous work the unknown distribution is assumed fixed which can lead to some problems with the convergence and consequently Monte Carlo errors of estimated distribution (e.g. Caron et al (2006)). The distribution is now time-varying and enjoys the benefits of rejuvenation for estimation of states and the unknown distribution at the propogation step.…”

Section: Particle Filtersmentioning

confidence: 99%

“…. , n. The sampler then resembles the approach taken by Fearnhead (2003) and Caron et al (2006) which is described as a Rao-Blackwellisation of the algorithm. A further step must be added to make this approach work.…”

Section: Rao-blackwellised Particle Filtering Algorithmmentioning

confidence: 99%

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The Ornstein–Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference

Griffin

2011

Journal of Statistical Planning and Inference

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This paper introduces a new class of time-varying, meaure-valued stochastic processes for Bayesian nonparametric inference. The class of priors generalizes the normalized random measure (Kingman 1975) construction for static problems. The unnormalized measure on any measureable set follows an Ornstein-Uhlenbeck process as described by BarndorffNielsen and Shephard (2001). Some properties of the normalized measure are investigated. A particle filter and MCMC schemes are described for inference. The methods are applied to an example in the modelling of financial data.

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Section: Particle Filtersmentioning

confidence: 99%

Section: Particle Filtersmentioning

confidence: 99%

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The Ornstein–Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference

Griffin

2011

Journal of Statistical Planning and Inference

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“…The prior on clustering variable vector is formulated by (2) in a recursive way, (2) where is the number of clusters in the assignment . In (2), is the number of observations that assigns to 1070-9908/$26.00 © 2010 IEEE cluster and is the positive valued 'novelty' parameter [8].…”

Section: Dirichlet Process Mixtures (Dpm)mentioning

confidence: 99%

“…I N recent years, there has been a surge of interest in Bayesian nonparametric methods in machine learning [1] and signal processing [2]. Here, researchers use highly structured and adaptive models where the model order is to be determined automatically by the data.…”

Section: Introductionmentioning

confidence: 99%

Annealed SMC Samplers for Nonparametric Bayesian Mixture Models

Ulker

Günsel

Cemgil

2011

IEEE Signal Process. Lett.

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Abstract-We develop a novel online algorithm for posterior inference in Dirichlet Process Mixtures (DPM). Our method is based on the Sequential Monte Carlo (SMC) samplers framework that generalizes sequential importance sampling approaches. Unlike the existing methods, the framework enables us to retrospectively update long trajectories in the light of recent observations and this leads to sophisticated clustering update schemes and annealing strategies that seem to prevent the algorithm to get stuck around a local mode. The performance has been evaluated on a Bayesian Gaussian density estimation problem with an unknown number of mixture components. Our simulations suggest that the proposed annealing strategy outperforms conventional samplers. It also provides significantly smaller Monte Carlo standard error with respect to particle filtering given comparable computational resources.Index Terms-Dirichlet process mixtures, particle filtering, sequential Monte Carlo methods.

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Estimation of structural changes in nonlinear time series models by using particle filters and genetic programming

Tokinaga

2015

Adaptive Control & Signal

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Several works have demonstrated detection of changes of state equations (called structural changes) based on statistical measures but have given no suggestions regarding the functional forms of the state equations after changes. This paper deals with the estimation of structural changes in nonlinear time series models by using particle filters, genetic programming (GP), and its applications. We consider the problems of state estimation from the observed time series that are generated based on nonlinear state equations. It is assumed that structural changes can be detected by some measure of likelihood and that the state equation after changes is modified from its current functional form. Individuals corresponding to functional forms in the GP pool are generated at random, and we apply the crossover operation between the current functional form and the individuals by giving possible multiple functional forms. Then, we have the optimal functional form among the possible functional forms generated by GP from the current form. As an application, we show the estimation of structural change for an artificially generated time series and also discuss the estimation of functional forms for a real economic time series before and after structural changes.In previous studies, several different indicators have been applied for the detection of structural changes in time series generation models. However, in this paper, we aim to estimate the time direction changes from the time of structural change. We assume a nonlinear equation in the PFs, is deformed, and is derived, from the current function .C /, to estimate these multiple deformed functions .A 1 ; A 2 ; :::/ by crossover processing using the GP method [10,[18][19][20][21][22][23][24]. That is, a set of functions, randomly generated in individual pool of GP, can be considered as opponent functions of the transformation of function C . By using the crossover procedure, we can only determine the number of individuals in a population pool that is a plurality of the functional form that is deformed from function C . The maximum likelihood, corresponding to the best functional form A m of the model, for which the error is minimized as a function of the changed structure, can be found by applying the PFs for all this generated function A i . As an application, we use artificial data to verify the effectiveness of this method, and furthermore, we applied this method to real-world time series data and discuss the estimation of the state equation after the structural change.In the following, Section 2 describes the basics of function estimation and extraction of structural changes when using PFs. Section 3 presents the equation estimation by function deformation and GP methods, and examples of the application are given in Section 4. Related worksIn the following, we summarize the related works regarding change detection of nonlinear dynamics and stress the strengths of our paper. Research on the estimation of structural changes (or change point detection) for nonlinear dynamics a...

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Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

Cited by 94 publications

References 44 publications

The Ornstein–Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference

The Ornstein–Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference

Annealed SMC Samplers for Nonparametric Bayesian Mixture Models

Estimation of structural changes in nonlinear time series models by using particle filters and genetic programming

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