Multilevel estimation of normalization constants using ensemble Kalman–Bucy filters

Ruzayqat, Hamza; Chada, Neil K.; Jasra, Ajay

doi:10.1007/s11222-022-10094-2

Cited by 5 publications

(6 citation statements)

References 31 publications

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“…e reason is that the improved vocal training method adopts factor Cauchy(0, 1) adjustment to sports training content and chooses di erent training strategies, which makes the training results more in line with the requirements [20].…”

Section: Resultsmentioning

confidence: 99%

“…In addition, the content of the exercise is not affected by the complexity, and the influence on vocal training is strong. The reason is that the improved vocal training method adopts factor Cauchy(0,1) adjustment to sports training content and chooses different training strategies, which makes the training results more in line with the requirements [ 20 ].…”

Section: Empirical Analysismentioning

confidence: 99%

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Analysis of the Influence of Sports on College Students’ Music Vocalization Training Based on Monte Carlo and Dynamic Adjustment Factor Algorithm

Hua

2022

Journal of Environmental and Public Health

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With the continuous improvement of people’s living standards, the requirements of music majors for their training standards are also increasing, which leads to the development of music training in the direction of intelligence. This paper discusses the problems of breathing, coordination, and muscle control ability in vocal training and puts forward a vocal training method based on dynamic adjustment factor and Monte Carlo algorithm to solve the difficult problem of vocal training for college students and understand the relationship between vocal training and exercise. Firstly, the sports training set and vocal pronunciation training set are constructed in the form of clustering, and the samples in the set are analyzed discretely to ensure that the samples conform to normal distribution; then, using the Monte Carlo algorithm analyzes the two sample sets and finds out the relationship between exercise and vocal training. Finally, according to breathing, coordination, muscle control ability, and other indicators, calculate the impact of exercise on vocal sound. MATLAB simulation shows that the method proposed in this paper can analyze the influence of exercise on vocal vocalization from the perspective of breathing, coordination, muscle control ability, and other indicators. The accuracy of judgment results is more than 95%, and the time is less than 1 min. All indicators are better than traditional vocal training methods (90%, 2 min), which shows the effectiveness of the method proposed in this paper.

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Section: Resultsmentioning

confidence: 99%

Section: Empirical Analysismentioning

confidence: 99%

Analysis of the Influence of Sports on College Students’ Music Vocalization Training Based on Monte Carlo and Dynamic Adjustment Factor Algorithm

Hua

2022

Journal of Environmental and Public Health

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“…Related to this, there exists another popular variant known as the deterministic transport EnKBF (DTEnKBF). However we omit such introducing it, as evidentially from [32], the numerics suggest the behavior of the DTEnKBF is different.…”

Section: Ensemble Kalman-bucy Filtermentioning

confidence: 99%

“…However there has been a growing interest in the EnKBF for both theory and applications. In particular the work of Del Moral and coauthors have aimed to analyze various theoretical properties [3,13,14], while other directions have been on applications to non-linear filtering and uncertainty quantification [6,9,32,35,36].…”

Section: Introductionmentioning

confidence: 99%

“…This will be done for two of the unbiased estimators introduced in [31] which are the singleterm estimator and the coupled sum estimator. In order to assess the performance of the unbiased estimator, we compare this with the multilevel EnKBF (MLEnKBF) [6,32]. The multilevel approach [17,18] is a variance reduction approach for Monte Carlo which has seen particular interest in the filtering community [23,26].…”

Section: Introductionmentioning

confidence: 99%

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Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters

Álvarez¹,

Chada²,

Jasra³

2022

Preprint

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In this article we consider the development of an unbiased estimator for the ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein-Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods.

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On the mathematical theory of ensemble (linear-Gaussian) Kalman–Bucy filtering

Bishop

Moral

2023

Math. Control Signals Syst.

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The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman–Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of individual particles and the flow of the sample covariance and the sample mean in continuous-time ensemble filtering. We consider these equations and their characteristics in a number of popular ensemble Kalman filtering variants. Given these equations, we study their asymptotic convergence to the optimal Bayesian filter. We also study in detail some non-asymptotic time-uniform fluctuation, stability, and contraction results on the sample covariance and sample mean (or sample error track). We focus on testable signal/observation model conditions, and we accommodate fully unstable (latent) signal models. We discuss the relevance and importance of these results in characterising the filter’s behaviour, e.g. it is signal tracking performance, and we contrast these results with those in classical studies of stability in Kalman–Bucy filtering. We also provide a novel (and negative) result proving that the bootstrap particle filter cannot track even the most basic unstable latent signal, in contrast with the ensemble Kalman filter (and the optimal filter). We provide intuition for how the main results extend to nonlinear signal models and comment on their consequence on some typical filter behaviours seen in practice, e.g. catastrophic divergence.

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Multilevel estimation of normalization constants using ensemble Kalman–Bucy filters

Cited by 5 publications

References 31 publications

Analysis of the Influence of Sports on College Students’ Music Vocalization Training Based on Monte Carlo and Dynamic Adjustment Factor Algorithm

Analysis of the Influence of Sports on College Students’ Music Vocalization Training Based on Monte Carlo and Dynamic Adjustment Factor Algorithm

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters

On the mathematical theory of ensemble (linear-Gaussian) Kalman–Bucy filtering

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