An application of sequential Monte Carlo samplers: an alternative to particle filters for non-linear non-gaussian sequential inference with zero process noise

2012 ◽  
Author(s):  
S. Maskell
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Particle Filters ◽  
Process Noise ◽  
Non Linear ◽  
Non Gaussian

scholarly journals Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation

2021 ◽  
Vol 28 (1) ◽  
pp. 23-41
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina ◽  
Jana de Wiljes
Keyword(s):  
Monte Carlo ◽  
Posterior Distribution ◽  
Sequential Monte Carlo ◽  
Optimal Transport ◽  
Hybrid Approach ◽  
Computational Cost ◽  
High Dimensional ◽  
Non Linear ◽  
Non Gaussian ◽  
Ensemble Transform

Abstract. Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark.

scholarly journals Hydrologic forecasting using artificial neural networks: a Bayesian sequential Monte Carlo approach

2010 ◽  
Vol 13 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Kuo-Lin Hsu
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Sequential Monte Carlo ◽  
Model Parameters ◽  
Ann Model ◽  
Streamflow Prediction ◽  
Streamflow Estimation ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
Non Gaussian

Sequential Monte Carlo (SMC) methods are known to be very effective for the state and parameter estimation of nonlinear and non-Gaussian systems. In this study, SMC is applied to the parameter estimation of an artificial neural network (ANN) model for streamflow prediction of a watershed. Through SMC simulation, the probability distribution of model parameters and streamflow estimation is calculated. The results also showed the SMC approach is capable of providing reliable streamflow prediction under limited available observations.

scholarly journals Applying sequential Monte Carlo methods into a distributed hydrologic model: lagged particle filtering approach with regularization

2011 ◽  
Vol 15 (10) ◽  
pp. 3237-3251 ◽  
Author(s):  
S. J. Noh ◽  
Y. Tachikawa ◽  
M. Shiiba ◽  
S. Kim
Keyword(s):  
Monte Carlo ◽  
Data Assimilation ◽  
Particle Filter ◽  
Particle Filtering ◽  
Sequential Monte Carlo ◽  
Hydrologic Model ◽  
State Variables ◽  
Process Noise ◽  
Distributed Hydrologic Model ◽  
Filtering Approach

Abstract. Data assimilation techniques have received growing attention due to their capability to improve prediction. Among various data assimilation techniques, sequential Monte Carlo (SMC) methods, known as "particle filters", are a Bayesian learning process that has the capability to handle non-linear and non-Gaussian state-space models. In this paper, we propose an improved particle filtering approach to consider different response times of internal state variables in a hydrologic model. The proposed method adopts a lagged filtering approach to aggregate model response until the uncertainty of each hydrologic process is propagated. The regularization with an additional move step based on the Markov chain Monte Carlo (MCMC) methods is also implemented to preserve sample diversity under the lagged filtering approach. A distributed hydrologic model, water and energy transfer processes (WEP), is implemented for the sequential data assimilation through the updating of state variables. The lagged regularized particle filter (LRPF) and the sequential importance resampling (SIR) particle filter are implemented for hindcasting of streamflow at the Katsura catchment, Japan. Control state variables for filtering are soil moisture content and overland flow. Streamflow measurements are used for data assimilation. LRPF shows consistent forecasts regardless of the process noise assumption, while SIR has different values of optimal process noise and shows sensitive variation of confidential intervals, depending on the process noise. Improvement of LRPF forecasts compared to SIR is particularly found for rapidly varied high flows due to preservation of sample diversity from the kernel, even if particle impoverishment takes place.

Parralelization of non-linear & non-Gaussian Bayesian state estimators (Particle filters)

2015 ◽  
Author(s):  
Amin Jarrah ◽  
Mohsin M. Jamali ◽  
S. S. S. Hosseini ◽  
Jaakko Astola ◽  
Moncef Gabbouj
Keyword(s):  
Particle Filters ◽  
State Estimators ◽  
Non Linear ◽  
Non Gaussian

An efficient sequential learning algorithm in regime-switching environments

2018 ◽  
Vol 23 (3) ◽  
Author(s):  
Jaeho Kim ◽  
Sunhyung Lee
Keyword(s):  
Monte Carlo ◽  
Regime Switching ◽  
Sequential Monte Carlo ◽  
Learning Algorithm ◽  
State Space Model ◽  
Gaussian State ◽  
Proposal Distribution ◽  
Novel Approach ◽  
Particle Learning ◽  
Non Gaussian

Abstract We provide a novel approach of estimating a regime-switching nonlinear and non-Gaussian state-space model based on a particle learning scheme. In particular, we extend the particle learning method in Liu, J., and M. West. 2001. “Combined Parameter and State Estimation in Simulation-Based Filtering.” In Sequential Monte Carlo Methods in Practice, 197–223. Springer. by constructing a new proposal distribution for the latent regime index variable that incorporates all available information contained in the current and past observations. The Monte Carlo simulation result implies that our approach categorically outperforms a popular existing algorithm. For empirical illustration, the proposed algorithm is used to analyze the underlying dynamics of US excess stock return.

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