On Blocks, Tempering and Particle MCMC for Systems Identification

Johansen, Adam M.

doi:10.1016/j.ifacol.2015.12.256

Cited by 9 publications

(7 citation statements)

References 15 publications

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“…The localisation approach to overcoming weight degeneracy when applying pfs to spatial models considered here could also be combined with other methods for improving pf performance in high-dimensional ssms. In particular tempering approaches split the usual single prediction and assimilation update per observation time into multiple updates which target a sequence of distributions bridging between the filtering distributions at adjacent observation times (Frei and Künsch, 2013;Johansen, 2015;Beskos et al, 2017;Svensson, Schön and Lindsten, 2018;Herbst and Schorfheide, 2019). Tempering could be paired with our framework to further improve its robustness to high-dimensional and strongly informative observations, with the use of multiple assimilation updates per observation time when tempering making the reduced computational cost and improved smoothness preservation of our approach particularly important.…”

Section: Discussionmentioning

confidence: 99%

A scalable optimal-transport based local particle filter

Graham,

Thiery

2019

Preprint

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Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large ensemble sizes for accurate estimates in complex spatial models. Localisation approaches, which perform local state updates by exploiting low dependence between variables at distant points, have been suggested as a potential resolution to this issue. Naively applying the resampling step of the particle filter locally however produces implausible spatially discontinuous states. The ensemble transform particle filter replaces resampling with an optimaltransport map and can be localised by computing maps for every spatial mesh node. The resulting local ensemble transport particle filter is however computationally intensive for dense meshes. We propose a new optimal-transport based local particle filter which computes a fixed number of maps independent of the mesh resolution and interpolates these maps across space, reducing the computation required and allowing it to be ensured particles remain spatially smooth. We numerically illustrate that, at a reduced computational cost, we are able to achieve the same accuracy as the local ensemble transport particle filter, and retain its improved robustness to non-Gaussianity and ability to quantify uncertainty when compared to local ensemble Kalman filters.

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Section: Discussionmentioning

confidence: 99%

A scalable optimal-transport based local particle filter

Graham,

Thiery

2019

Preprint

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“…Moreover for PFs, the ideal proposal distribution from which prior weights are sampled, must be different from the posterior to allow effective estimation (Godsill & Clapp, 2001). However, if this difference is too large then the importance weights will be close to zero for frequent outcomes and close to one for rare values (Johansen, 2015). Consequently, the state estimates obtained will be dominated by a small subset of the Markov chain (Woodhead, 2007).…”

Section: Methodsmentioning

confidence: 99%

A Mutual Information‐Based Likelihood Function for Particle Filter Flood Extent Assimilation

Dasgupta

Hostache

Ramsankaran

et al. 2021

Water Resources Research

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Accurate flood inundation forecasts have the potential to minimize socioeconomic losses, but uncertainties in inflows propagated from the precipitation forecasts result in large prediction errors. Recent studies suggest that by assimilating independent flood observations, inherent uncertainty in hydraulic flood inundation modeling can be mitigated. Satellite observations from Synthetic Aperture Radar (SAR) sensors, with demonstrated flood monitoring capability, can thus be used to reduce flood forecast uncertainties through assimilation. However, researchers have struggled to develop an appropriate cost function to determine the innovation to be applied at each assimilation time step. Thus, a novel likelihood function based on mutual information (MI) is proposed here, for use with a particle filter‐based (PF) flood extent assimilation framework. Using identical twin experiments, synthetic SAR‐based probabilistic flood extents were assimilated into the hydraulic model LISFLOOD‐FP using the proposed PF‐MI algorithm. The 2011 flood event in the Clarence Catchment, Australia was used for this study. The impact of assimilating flood extents was evaluated in terms of subsequent flood extent evolution, floodplain water depths, flow velocities and channel water levels (WLs). Water depth and flow velocity simulations improved by ∼60% over the open loop on an average and persisted for up to 7 days, following the sequential assimilation of two post‐peak flood extent observations. Flood extents and channel WLs also showed mean improvements of ∼10% and ∼80% in accuracy, respectively, indicating that the proposed MI likelihood function can improve flood extent assimilation.

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“…"bootstrap proposal" and could be mitigated in the same way as standard particle filters by seeking to design (marginal) proposal distributions which incorporate the influence of observations. In addition, this phenomenon can be mitigated with the use of (adaptive) tempering, as shown in, e.g., Jasra et al (2010); Johansen (2015); Wang et al (2020); Zhou et al (2016) for standard SMC and Lindsten et al (2017, Section 4.2) for DaC-SMC.…”

Section: Adaptive Lightweight Mixture Resamplingmentioning

confidence: 99%

A Divide and Conquer Sequential Monte Carlo Approach to High Dimensional Filtering

Crucinio¹,

Johansen²

2023

STAT SINICA

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We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full filtering distribution. It is less dependent upon factorization of transition densities and observation likelihoods than competing approaches and can be applied to a broader class of models. Performance is compared with state-of-the-art methods on a benchmark problem and it is demonstrated that the proposed method is broadly comparable in settings in which those methods are applicable, and that it can be applied in settings in which they cannot.

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On Blocks, Tempering and Particle MCMC for Systems Identification

Cited by 9 publications

References 15 publications

A scalable optimal-transport based local particle filter

A scalable optimal-transport based local particle filter

A Mutual Information‐Based Likelihood Function for Particle Filter Flood Extent Assimilation

A Divide and Conquer Sequential Monte Carlo Approach to High Dimensional Filtering

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