Particle filters for state-space models with the presence of unknown static parameters

Storvik, Geir

doi:10.1109/78.978383

Cited by 372 publications

(287 citation statements)

References 22 publications

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“…This problem exhibits a nonlinear and non-Gaussian challenging setting, and it has been inspired by a variety of nonlinear filtering studies (e.g., refs. 13,14).…”

Section: Toy Examplementioning

confidence: 99%

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Empirical intrinsic geometry for nonlinear modeling and time series filtering

Talmon

Coifman

2013

Proc. Natl. Acad. Sci. U.S.A.

107

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In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.anisotropic diffusion | manifold learning | signal processing I n recent years, there has been much progress in the development of new methods for parameterizing and embedding highdimensional data in a low-dimensional space (1-4). The method proposed by Singer and Coifman (5) is of particular interest because the data are assumed to be inaccessible and can be observed only via unknown nonlinear functions. By integrating local principal components with diffusion maps, the approach of Singer and Coifman (5) provides modeling of the underlying parametric manifold, whereas classical manifold learning methods provide a parameterization of the observable manifold. However, geometric methods usually suffer from two significant disadvantages. First, in many natural systems, the mapping of the low-dimensional data into a subset of high-dimensional observations is stochastic. In addition, a random measurement noise usually corrupts the observations. Thus, the geometry of the observations may not convey the appropriate information on the underlying parametric manifold. Second, these methods provide modeling to a given dataset and do not model a stream of new incoming measurements well.In this paper, we propose a framework for sequential processing of time series based on empirical intrinsic geometric models. We adopt the nonlinear filtering formalism and propose a method consisting of two steps: novel data-driven modeling of stochastic data, which is resilient to noise as well as invariant to the measurement modality, and Bayesian filtering of new incoming measurements based on the learned model. High-dimensional time series often exhibit highly redundant representations and can be compactly represented by a dynamical process on a lowdimensional manifold. Thus, in the first stage, we reveal the lowdimensional manifold and infer the underlying process using anisotropic diffusion. The proposed approach relies on the observation that the local s...

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“…This problem exhibits a nonlinear and non-Gaussian challenging setting, and it has been inspired by a variety of nonlinear filtering studies (e.g., refs. 13,14).…”

Section: Toy Examplementioning

confidence: 99%

“…ts φ s i ; [13] describes an efficient extension of the spectral representation to a new measurement at time t without applying additional eigendecomposition. We note that Eq.…”

Section: Intrinsic Modelingmentioning

confidence: 99%

Empirical intrinsic geometry for nonlinear modeling and time series filtering

Talmon

Coifman

2013

Proc. Natl. Acad. Sci. U.S.A.

107

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“…Moreover unlike in these works, in MAPF, the overall computational cost is kept constant, chosen in advance by the user. Other related and well-known approaches for the joint purpose of sequential tracking and parameter estimation are given in [2,35]. In [14], the Kolmogorov-Smirnov test is applied for testing a dynamic equation in a state-space model.…”

Section: Introductionmentioning

confidence: 99%

Cooperative parallel particle filters for online model selection and applications to urban mobility

Martino

Read

Elvira

et al. 2017

Digital Signal Processing

136

112

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We design a sequential Monte Carlo scheme for the dual purpose of Bayesian inference and model selection. We consider the application context of urban mobility, where several modalities of transport and different measurement devices can be employed. Therefore, we address the joint problem of online tracking and detection of the current modality. For this purpose, we use interacting parallel particle filters, each one addressing a different model. They cooperate for providing a global estimator of the variable of interest and, at the same time, an approximation of the posterior density of each model given the data. The interaction occurs by a parsimonious distribution of the computational effort, with online adaptation for the number of particles of each filter according to the posterior probability of the corresponding model. The resulting scheme is simple and flexible. We have tested the novel technique in different numerical experiments with artificial and real data, which confirm the robustness of the proposed scheme.

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“…We show that different models have different VaR requirements, 2 There has already been progress towards tackling parameter learning in general state-space models. See Liu and West (2001), Gilks and Berzouini (2001), Storvik (2002), Flury andShephard (2009), andCarvalho et al (2010). For discussion of these methods, see Fulop and Li (2010).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

Fülöp

2011

SSRN Journal

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The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensity remain difficult to identify.

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Particle filters for state-space models with the presence of unknown static parameters

Cited by 372 publications

References 22 publications

Empirical intrinsic geometry for nonlinear modeling and time series filtering

Empirical intrinsic geometry for nonlinear modeling and time series filtering

Cooperative parallel particle filters for online model selection and applications to urban mobility

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

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