scholarly journals Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study

2010 ◽  
Vol 37 (8) ◽  
Author(s):  
Xiao-Ming Hu ◽  
Fuqing Zhang ◽  
John W. Nielsen-Gammon
Keyword(s):  
Parameter Estimation ◽  
Mesoscale Model ◽  
Real Data ◽  
Model Error

scholarly journals Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

2015 ◽  
Vol 143 (5) ◽  
pp. 1568-1582 ◽  
Author(s):  
Juan Ruiz ◽  
Manuel Pulido
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Model Error ◽  
Forecast Skill ◽  
Moist Convection ◽  
Treatment Techniques ◽  
Correction Technique ◽  
Error Treatment ◽  
Data Assimilation System ◽  
Assimilation System

Abstract This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

Continuous Autoregressive Moving Average Models

2021 ◽  
pp. 118-141
Author(s):  
Yakup Ari
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

scholarly journals Regularized Parameter Estimation in High-Dimensional Gaussian Mixture Models

2011 ◽  
Vol 23 (6) ◽  
pp. 1605-1622 ◽  
Author(s):  
Lingyan Ruan ◽  
Ming Yuan ◽  
Hui Zou
Keyword(s):  
Parameter Estimation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Model Based Clustering ◽  
Text Type ◽  
Effective Dimensionality

Finite gaussian mixture models are widely used in statistics thanks to their great flexibility. However, parameter estimation for gaussian mixture models with high dimensionality can be challenging because of the large number of parameters that need to be estimated. In this letter, we propose a penalized likelihood estimator to address this difficulty. The [Formula: see text]-type penalty we impose on the inverse covariance matrices encourages sparsity on its entries and therefore helps to reduce the effective dimensionality of the problem. We show that the proposed estimate can be efficiently computed using an expectation-maximization algorithm. To illustrate the practical merits of the proposed method, we consider its applications in model-based clustering and mixture discriminant analysis. Numerical experiments with both simulated and real data show that the new method is a valuable tool for high-dimensional data analysis.

Combined state-parameter estimation with the LETKF for convective-scale weather forecasting

2020 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

<p>We investigate the feasibility of addressing model error by perturbing and  estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly-operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to six hours of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.</p>

scholarly journals Detection of arterial wall abnormalities via Bayesian model selection

2018 ◽  
Author(s):  
Karen Larson ◽  
Clark Bowman ◽  
Costas Papadimitriou ◽  
Petros Koumoutsakos ◽  
Anastasios Matzavinos
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Parallel Implementation ◽  
Real Data ◽  
Physical Models ◽  
Patient Specific ◽  
Small Scale ◽  
Tree Model ◽  
Arterial Tree ◽  
Flow Models

AbstractPatient-specific modeling of hemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for hemodynamical flow models.

scholarly journals Detection of arterial wall abnormalities via Bayesian model selection

2019 ◽  
Vol 6 (10) ◽  
pp. 182229
Author(s):  
Karen Larson ◽  
Clark Bowman ◽  
Costas Papadimitriou ◽  
Petros Koumoutsakos ◽  
Anastasios Matzavinos
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Parallel Implementation ◽  
Real Data ◽  
Physical Models ◽  
Patient Specific ◽  
Small Scale ◽  
Tree Model ◽  
Arterial Tree ◽  
Flow Models

Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for haemodynamical flow models.

scholarly journals Probabilistic moveout analysis by time warping

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. U1-U20
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel ◽  
Jeannot Trampert ◽  
William Burnett ◽  
Thomas Hess
Keyword(s):  
Parameter Estimation ◽  
Posterior Probability ◽  
Model Building ◽  
Probability Distributions ◽  
Real Data ◽  
Inversion Method ◽  
Time Warping ◽  
Anisotropic Models ◽  
Trade Offs ◽  
Set Up

Parameter estimation from reflection moveout analysis represents one of the most fundamental problems in subsurface model building. We have developed an efficient moveout inversion method based on the process of automatic flattening of common-midpoint (CMP) gathers using local slopes. We find that as a by-product of this flattening process, we can also estimate reflection traveltimes corresponding to the flattened CMP gathers. This traveltime information allows us to construct a highly overdetermined system and subsequently invert for moveout parameters including normal-moveout velocities and quartic coefficients related to anisotropy. We use the 3D generalized moveout approximation (GMA), which can accurately capture the effects of complex anisotropy on reflection traveltimes as the basis for our moveout inversion. Due to the cheap forward traveltime computations by GMA, we use a Monte Carlo inversion scheme for improved handling of the nonlinearity between the reflection traveltimes and moveout parameters. This choice also allows us to set up a probabilistic inversion workflow within a Bayesian framework, in which we can obtain the posterior probability distributions that contain valuable statistical information on estimated parameters such as uncertainty and correlations. We use synthetic and real data examples including the data from the SEAM Phase II unconventional reservoir model to demonstrate the performance of our method and discuss insights into the problem of moveout inversion gained from analyzing the posterior probability distributions. Our results suggest that the solutions to the problem of traveltime-only moveout inversion from 2D CMP gathers are relatively well constrained by the data. However, parameter estimation from 3D CMP gathers associated with more moveout parameters and complex anisotropic models are generally nonunique, and there are trade-offs among inverted parameters, especially the quartic coefficients.

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