Point-Mass Filter: Density Specific Grid Design and Implementation

Matoušek, Jakub; Duník, Jindřich; Straka, Ondřej

doi:10.1007/978-3-030-85318-1_64

Cited by 3 publications

(12 citation statements)

References 17 publications

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“…As can be seen in [24], the DSG design significantly outperforms the standard equidistant grid design if the underlying conditional PDF is unimodal, rather symmetric, and light-tailed. If any of the mentioned properties are violated, the DSG benefit is marginal.…”

Section: Density Specific Grid Designmentioning

confidence: 90%

“…The DSG design [24], is based on an unequally spaced placement of the fixed number of points over the PDF support R to be approximated. The main idea is to approximate the PDF, where the volume of the PDF is significant or significantly varying by a denser grid (as in this area, a slope of the PDF is expected to be significant) and the tail of the PDF by a sparser grid (as the tail is flat).…”

Section: Density Specific Grid Designmentioning

confidence: 99%

“…The global filters are capable of estimating the state of a strongly nonlinear or non-Gaussian system but usually at the cost of higher computational demands. Among these, the Gaussian sum filter [19], the particle filter [20], and the point-mass filter [21][22][23][24] have attracted a considerable attention.…”

Section: Introductionmentioning

confidence: 99%

“…Design of the Rao-Blackwellized (or marginalized) PMF [23,25], • Efficient convolution in the PMF prediction step [21,22,24,[26][27][28][29].…”

mentioning

confidence: 99%

“…Recently, a novel method for the efficient convolution, based on the the density-specific grid (DSG) design, was proposed [24]. Compared to other methods (typically assuming one equidistant grid), the DSG assumes two different grids (each with different properties);…”

mentioning

confidence: 99%

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Density Difference Grid Design in a Point-Mass Filter

2020

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The paper deals with the Bayesian state estimation of nonlinear stochastic dynamic systems. The stress is laid on the point-mass filter, solving the Bayesian recursive relations for the state estimate conditional density computation using the deterministic grid-based numerical integration method. In particular, the grid design is discussed and the novel density difference grid is proposed. The proposed grid design covers such regions of the state-space where the conditional density is significantly spatially varying, by the dense grid. In other regions, a sparse grid is used to keep the computational complexity low. The proposed grid design is thoroughly discussed, analyzed, and illustrated in a numerical study.

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Section: Density Specific Grid Designmentioning

confidence: 90%

Section: Density Specific Grid Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Design of the Rao-Blackwellized (or marginalized) PMF [23,25], • Efficient convolution in the PMF prediction step [21,22,24,[26][27][28][29].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Density Difference Grid Design in a Point-Mass Filter

2020

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A point mass proposal method for Bayesian state-space model fitting

et al. 2023

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State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of the data given the parameters is not available in closed-form. One approach is to jointly sample the latent states and model parameters via Markov chain Monte Carlo (MCMC) and/or sequential Monte Carlo approximation. These methods can be inefficient, mixing poorly when there are many highly correlated latent states or parameters, or when there is a high rate of sample impoverishment in the sequential Monte Carlo approximations. We propose a novel block proposal distribution for Metropolis-within-Gibbs sampling on the joint latent state and parameter space. The proposal distribution is informed by a deterministic hidden Markov model (HMM), defined such that the usual theoretical guarantees of MCMC algorithms apply. We discuss how the HMMs are constructed, the generality of the approach arising from the tuning parameters, and how these tuning parameters can be chosen efficiently in practice. We demonstrate that the proposed algorithm using HMM approximations provides an efficient alternative method for fitting state-space models, even for those that exhibit near-chaotic behavior.

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