A uniformly convergent adaptive particle filter

Particle filters are Monte Carlo methods that aim to approximate the optimal filter of a partially observed Markov chain. In this paper, we study the case in which the transition kernel of the Markov chain depends on unknown parameters: we construct a particle filter for the simultaneous estimation of the parameter and the partially observed Markov chain (adaptive estimation) and we prove the convergence of this filter to the correct optimal filter, as time and the number of particles go to infinity. The filter presented here generalizes Del Moral's Monte Carlo particle filter.

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A Monte Carlo approach for determining cluster evaporation rates from concentration measurements

10.5194/acp-2016-168 ◽

2016 ◽

Author(s):

Oona Kupiainen-Määttä

Keyword(s):

Experimental Data ◽

Monte Carlo ◽

Markov Chain ◽

Sulfuric Acid ◽

Markov Chain Monte Carlo ◽

Mass Spectrometer ◽

Large Fraction ◽

Cluster Formation ◽

Unknown Parameters ◽

Ammonia Clusters

Abstract. Evaporation rates of small negatively charged sulfuric acid–ammonia clusters are determined by combining detailed cluster formation simulations with cluster distributions measured at CLOUD. The analysis is performed by varying the evaporation rates with Markov chain Monte Carlo (MCMC), running cluster formation simulations with each new set of evaporation rates and comparing the obtained cluster distributions to the measurements. In a second set of simulations, the fragmentation of clusters in the mass spectrometer due to energetic collisions is studied by treating also the fragmentation probabilities as unknown parameters and varying them with MCMC. This second set of simulations results in a better fit to the experimental data, suggesting that a large fraction of the observed HSO4− and HSO4− ⋅ H2SO4 signals may result from fragmentation of larger clusters, most importantly the HSO4− ⋅ (H2SO4)2 trimer.

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Genetic Operator-Based Particle Filter Combined with Markov Chain Monte Carlo for Data Assimilation in a Crop Growth Model

Agriculture ◽

10.3390/agriculture10120606 ◽

2020 ◽

Vol 10 (12) ◽

pp. 606

Author(s):

Alaa Jamal ◽

Raphael Linker

Keyword(s):

Monte Carlo ◽

Parameter Estimation ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Data Assimilation ◽

Particle Filter ◽

Sequential Estimation ◽

Measurement Noise ◽

Genetic Operators ◽

True Value

Particle filter has received increasing attention in data assimilation for estimating model states and parameters in cases of non-linear and non-Gaussian dynamic processes. Various modifications of the original particle filter have been suggested in the literature, including integrating particle filter with Markov Chain Monte Carlo (PF-MCMC) and, later, using genetic algorithm evolutionary operators as part of the state updating process. In this work, a modified genetic-based PF-MCMC approach for estimating the states and parameters simultaneously and without assuming Gaussian distribution for priors is presented. The method was tested on two simulation examples on the basis of the crop model AquaCrop-OS. In the first example, the method was compared to a PF-MCMC method in which states and parameters are updated sequentially and genetic operators are used only for state adjustments. The influence of ensemble size, measurement noise, and mutation and crossover parameters were also investigated. Accurate and stable estimations of the model states were obtained in all cases. Parameter estimation was more challenging than state estimation and not all parameters converged to their true value, especially when the parameter value had little influence on the measured variables. Overall, the proposed method showed more accurate and consistent parameter estimation than the PF-MCMC with sequential estimation, which showed highly conservative behavior. The superiority of the proposed method was more pronounced when the ensemble included a large number of particles and the measurement noise was low.

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Quasi-Monte Carlo Gaussian Particle Filtering Acceleration Using CUDA

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.130-134.3311 ◽

2011 ◽

Vol 130-134 ◽

pp. 3311-3315

Author(s):

Nai Gao Jin ◽

Fei Mo Li ◽

Zhao Xing Li

Keyword(s):

Monte Carlo ◽

Particle Filter ◽

Particle Filtering ◽

Parallel Implementation ◽

Accurate Estimation ◽

Quasi Monte Carlo ◽

Speedup Ratio ◽

Non Gaussian ◽

Gpu Implementation ◽

Number Of Particles

A CUDA accelerated Quasi-Monte Carlo Gaussian particle filter (QMC-GPF) is proposed to deal with real-time non-linear non-Gaussian problems. GPF is especially suitable for parallel implementation as a result of the elimination of resampling step. QMC-GPF is an efficient counterpart of GPF using QMC sampling method instead of MC. Since particles generated by QMC method provides the best-possible distribution in the sampling space, QMC-GPF can make more accurate estimation with the same number of particles compared with traditional particle filter. Experimental results show that our GPU implementation of QMC-GPF can achieve the maximum speedup ratio of 95 on NVIDIA GeForce GTX 460.

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A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder

Heat Transfer Engineering ◽

10.1080/01457632.2017.1305823 ◽

2017 ◽

Vol 39 (4) ◽

pp. 339-352 ◽

Cited By ~ 4

Author(s):

Harsha Kumar ◽

Sharath Kumar ◽

Nagarajan Gnanasekaran ◽

Chakravarthy Balaji

Keyword(s):

Heat Transfer ◽

Monte Carlo ◽

Markov Chain ◽

Heat Transfer Coefficient ◽

Markov Chain Monte Carlo ◽

Transfer Coefficient ◽

Heat Generation ◽

Simultaneous Estimation

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Parameter Estimation Using Markov Chain Monte Carlo Method in Mechanistic Modeling of Tool Wear During Milling

Volume 2: Materials; Biomanufacturing; Properties, Applications and Systems; Sustainable Manufacturing ◽

10.1115/msec2015-9357 ◽

2015 ◽

Cited By ~ 3

Author(s):

Farbod Akhavan Niaki ◽

Durul Ulutan ◽

Laine Mears

Keyword(s):

Monte Carlo ◽

Parameter Estimation ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Tool Wear ◽

End Milling ◽

Mechanistic Modeling ◽

Unknown Parameters ◽

Workpiece Material ◽

Machining Parameter

Several models have been proposed to describe the relationship between cutting parameters and machining outputs such as cutting forces and tool wear. However, these models usually cannot be generalized, due to the inherent uncertainties that exist in the process. These uncertainties may originate from machining, workpiece material composition, and measurements. A stochastic approach can be utilized to compensate for the lack of certainty in machining, particularly for tool wear evolution. The Markov Chain Monte Carlo (MCMC) method is a powerful tool for addressing uncertainties in machining parameter estimation. The Hybrid Metropolis-Gibbs algorithm has been chosen in this work to estimate the unknown parameters in a mechanistic tool wear model for end milling of difficult-to-machine alloys. The results show a good potential of the Markov Chain Monte Carlo modeling in prediction of parameters in the presence of uncertainties.

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The Alive Particle Filter and Its Use in Particle Markov Chain Monte Carlo

Stochastic Analysis and Applications ◽

10.1080/07362994.2015.1060892 ◽

2015 ◽

Vol 33 (6) ◽

pp. 943-974 ◽

Cited By ~ 10

Author(s):

Pierre Del Moral ◽

Ajay Jasra ◽

Anthony Lee ◽

Christopher Yau ◽

Xiaole Zhang

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Particle Filter

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Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods

10.20944/preprints201907.0318.v1 ◽

2019 ◽

Author(s):

Yasushi Ota ◽

Yu Jiang

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Bayesian Inference ◽

Financial Markets ◽

Sampling Strategy ◽

Measured Data ◽

Mcmc Algorithm ◽

Unknown Parameters ◽

Posterior Probability Density

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

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