Sequential Bayesian inference for implicit hidden Markov models and current limitations

Jacob, Pierre

doi:10.1051/proc/201551002

Cited by 11 publications

(13 citation statements)

References 95 publications

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“…Our last example involves a model of plankton-zooplankton dynamics taken from Jones et al (2010), in which the transition density is intractable (Bretó et al, 2009;Jacob, 2015). The bootstrap particle filter is still implementable, and one can either keep the entire trajectories of the particle filter, or perform fixed-lag approximations to perform smoothing.…”

Section: Prey-predator Modelmentioning

confidence: 99%

Smoothing With Couplings of Conditional Particle Filters

Jacob

Lindsten

Schön

2019

Journal of the American Statistical Association

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In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and confidence intervals can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly-informative observations, and a realistic Lotka-Volterra model with an intractable transition density.

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Section: Prey-predator Modelmentioning

confidence: 99%

Smoothing With Couplings of Conditional Particle Filters

Jacob

Lindsten

Schön

2019

Journal of the American Statistical Association

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“…Traditionally, resampling is executed when the ESS drops below a given threshold, N T . The threshold is expressed as a proportion of the number of particles and is sometimes defaulted to 50% [14]. This is because most resampling algorithms are serial by nature and create a bottleneck.…”

Section: B Resamplingmentioning

confidence: 99%

Improved Parallel Resampling Methods for Particle Filtering

Nicely

Wells

2019

IEEE Access

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Particle filter techniques are common methods used to estimate the evolving state of nonlinear, non-Gaussian time-variant systems by utilizing a periodic sequence of noisy measurements. The accuracy of particle filter methods has often been shown to be superior to other state estimation techniques, such as the extended Kalman filter (EKF), for many applications. Unfortunately, the high computational cost and highly nondeterministic runtime behavior of particle filters often preclude their use in hard, real-time environments, where filter response must meet the strict timing requirements of the application. Particle filter algorithms are composed of three main stages: prediction, update, and resampling. General purpose graphics processing units (GPGPUs) have been successfully employed in previous research to accelerate the computation of both the prediction and update stages by exploiting their natural fine-grain parallelism. This research focuses on accelerating the resampling stage for GPGPU execution, which has been much more difficult to parallelize due to it's apparent inherent sequentially. This paper introduces a novel GPGPU implementation of the systematic and stratified resampling algorithms that exploit the monotonically increasing nature of the prefix-sum and the evolutionary nature of the particle weighting process to allow the re-indexing portion of the algorithms to occur in a two-phase, multi-threaded manner. This resulting measured factor of performance improvement for the systematic and stratified algorithms was 15x and 32x, respectively, over the serial implementations. INDEX TERMS Graphics processing units, parallel algorithms, parallel architectures, parallel programming, particle filters, state estimation, resampling.

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“…We investigate the performance of the correlated particle marginal Metropolis-Hastings algorithm and of the Rhee-Glynn smoother for a nonlinear non-Gaussian model. We consider the Plankton-Zooplankton model of Jones et al (2010), which is an example of an implicit model: the transition density is intractable (Bretó et al, 2009;Jacob, 2015). The hidden state x t = (p t , z t ) represents the population size of phytoplankton and zooplankton, and the transition from time t to t + 1 is Figure 4: Confidence intervals on the smoothing means, obtained with R = 10, 000 Rhee-Glynn smoothers (left), and bootstrap particle filters (right).…”

Section: Numerical Experiments In a Prey-predator Modelmentioning

confidence: 99%

Coupling of Particle Filters

Jacob,

Lindsten,

Schön

2016

Preprint

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Particle filters provide Monte Carlo approximations of intractable quantities such as pointwise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some parameter or input varies. To facilitate such comparisons, we introduce and study methods to couple two particle filters in such a way that the correlation between the two underlying particle systems is increased. The motivation stems from the classic variance reduction technique of positively correlating two estimators. The key challenge in constructing such a coupling stems from the discontinuity of the resampling step of the particle filter. As our first contribution, we consider coupled resampling algorithms. Within bootstrap particle filters, they improve the precision of finite-difference estimators of the score vector and boost the performance of particle marginal Metropolis-Hastings algorithms for parameter inference. The second contribution arises from the use of these coupled resampling schemes within conditional particle filters, allowing for unbiased estimators of smoothing functionals. The result is a new smoothing strategy that operates by averaging a number of independent and unbiased estimators, which allows for 1) straightforward parallelization and 2) the construction of accurate error estimates. Neither of the above is possible with existing particle smoothers.

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Sequential Bayesian inference for implicit hidden Markov models and current limitations

Cited by 11 publications

References 95 publications

Smoothing With Couplings of Conditional Particle Filters

Smoothing With Couplings of Conditional Particle Filters

Improved Parallel Resampling Methods for Particle Filtering

Coupling of Particle Filters

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