scholarly journals Globally optimal parameter estimates for nonlinear diffusions

2010 ◽  
Vol 38 (1) ◽  
pp. 215-245 ◽  
Author(s):  
Aleksandar Mijatović ◽  
Paul Schneider
Keyword(s):  
Optimal Parameter ◽  
Parameter Estimates ◽  
Nonlinear Diffusions

scholarly journals Bayesian calibration of firn densification models

2020 ◽  
Author(s):  
Vincent Verjans ◽  
Amber Alexandra Leeson ◽  
Christopher Nemeth ◽  
C. Max Stevens ◽  
Peter Kuipers Munneke ◽  
...  
Keyword(s):  
Mass Balance ◽  
Optimal Parameter ◽  
Ice Sheet ◽  
Calibration Method ◽  
Parameter Estimates ◽  
Age Difference ◽  
Bayesian Calibration ◽  
Independent Observations ◽  
Ice Sheet Mass Balance ◽  
Parameter Values

Abstract. Firn densification modelling is key to understanding ice sheet mass balance, ice sheet surface elevation change, and the age difference between ice and the air in enclosed air bubbles. This has resulted in the development of many firn models, all relying to a certain degree on parameter calibration against observed data. We present a novel Bayesian calibration method for these parameters, and apply it to three existing firn models. Using an extensive dataset of firn cores from Greenland and Antarctica, we reach optimal parameter estimates applicable to both ice sheets. We then use these to simulate firn density and evaluate against independent observations. Our simulations show a significant decrease (25 and 55 %) in observation-model discrepancy for two models and a small increase (11 %) for the third. As opposed to current methods, the Bayesian framework allows for robust uncertainty analysis related to parameter values. Based on our results, we review some inherent model assumptions and demonstrate how model- and parameter-related uncertainties potentially affect ice sheet mass balance assessments.

Gradient iterative algorithm for rational models based on Gram-Schmidt orthogonalization method

2021 ◽  
Author(s):  
Yan Pu ◽  
Jing Chen ◽  
Yongqing Yang ◽  
Quanmin Zhu
Keyword(s):  
Iterative Algorithm ◽  
Large Scale ◽  
Optimal Parameter ◽  
Parameter Estimates ◽  
Large Scale Systems ◽  
Rational Models ◽  
Orthogonalization Method ◽  
The Matrix ◽  
Schmidt Orthogonalization ◽  
Information Vector

Abstract An improved gradient iterative algorithm, termed as Gram-Schmidt orthogonalization based gradient iterative algorithm, is proposed for rational models in this paper. The algorithm can obtain the optimal parameter estimates in one iteration for the reason that the information vectors obtained by using the Gram-Schmidt orthogonalization method are independent of each other. Compared to the least squares algorithm and the traditional gradient iterative algorithm, the proposed algorithm does not require the matrix inversion and eigenvalue calculation, thus it can be applied to nonlinear systems with complex structures or large-scale systems. Since the information vector of the rational models contains the latest output that is correlated with the noise, a biased compensation Gram-Schmidt orthogonalization based gradient iterative algorithm is introduced, by which the unbiased parameter estimates can be obtained. Two simulated examples are applied to demonstrate the efficiency of the proposed algorithm.

Evaluation of Hottest-Spot Temperature Models using Field Measured Transformer Data

2011 ◽  
Vol 12 (5) ◽  
Author(s):  
Oluwaseun Amoda ◽  
Daniel J Tylavsky ◽  
Gary McCulla ◽  
Wesley Knuth
Keyword(s):  
Linear Regression ◽  
Nonlinear Model ◽  
Nonlinear Regression ◽  
Field Data ◽  
Linear Models ◽  
Optimal Parameter ◽  
Original Model ◽  
Parameter Estimates ◽  
Modified Model ◽  
Spot Temperature

The acceptability of two hottest-spot temperature models is assessed in this paper. The first model, contained in the IEEE loading guide, is shown not to accurately account for the effects of the top-oil temperature (TOT) variation on the hottest-spot temperature. A new model which accounts for TOT variation is derived. The original and modified models are linearized and fitted to field data using linear regression to obtain optimal parameter estimates. Comparison of the parameter estimates and prediction simulations show that even though the original model is not structurally accurate, it, as well as the modified model, are acceptable for prediction purposes. The method of nonlinear regression is also used in an attempt to find better parameter estimates for the nonlinear modified model. It is shown that parameter estimates for the nonlinear model are inferior to those obtained for the linear models.

scholarly journals Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width

2013 ◽  
Vol 9 (1) ◽  
pp. 615-645 ◽  
Author(s):  
S. E. Tolwinski-Ward ◽  
K. J. Anchukaitis ◽  
M. N. Evans
Keyword(s):  
Tree Ring ◽  
Optimal Parameter ◽  
Ring Width ◽  
Physical Space ◽  
The United States ◽  
Parameter Estimates ◽  
Tree Ring Width ◽  
Multidimensional Parameter ◽  
Parameter Values ◽  
Insight Into

Abstract. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width. The scheme also provides information about the uncertainty of the parameter estimates, as well as the uncertainty of VS-Lite itself. By inferring VS-Lite's parameters for synthetically-generated ring-width series at several hundred sites across the United States, we show that the Bayesian algorithm is skillful and robust to climatic nonstationarity over the interval tested. We also infer optimal parameter values for modeling observed ring-width data at the same network of sites. The estimated parameter values cluster in physical space, and their locations in multidimensional parameter space provide insight into the dominant climatic controls on modeled tree-ring growth at each site.

Simultaneous Determination of Skeletal Model Parameter Values, Motions, and Controls From Noisy Measurement Data

2008 ◽  
Author(s):  
Michael G. Fattey ◽  
Benjamin J. Fregly
Keyword(s):  
Inverse Dynamics ◽  
Optimal Parameter ◽  
Measurement Data ◽  
Biomechanical Model ◽  
Optimization Techniques ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Parameter ◽  
Multi Level ◽  
Cadaver Studies

Accurate model parameter value and motion determination is important for obtaining reliable results from inverse dynamics analyses of gait. If the model parameters do not properly match their true values, the predicted motions and loads may lose their clinical significance [1]. Typical approaches to biomechanical model parameter estimation have included the use of scaling rules based on cadaver studies [2] and the use of multi-level optimization routines [3,4]. However, scaling rules do not provide optimal parameter estimates, and multi-level optimization techniques are computationally expensive.

scholarly journals Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width

2013 ◽  
Vol 9 (4) ◽  
pp. 1481-1493 ◽  
Author(s):  
S. E. Tolwinski-Ward ◽  
K. J. Anchukaitis ◽  
M. N. Evans
Keyword(s):  
Tree Ring ◽  
Optimal Parameter ◽  
Full Range ◽  
Ring Width ◽  
Physical Space ◽  
Estimation Procedure ◽  
The United States ◽  
Parameter Estimates ◽  
Tree Ring Width ◽  
Parameter Values

Abstract. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width for a particular chronology and its local climatology. The scheme also provides information about the uncertainty of the parameter estimates, as well as the model error in representing the observed proxy time series. By inferring VS-Lite's parameters independently for synthetically generated ring-width series at several hundred sites across the United States, we show that the algorithm is skillful. We also infer optimal parameter values for modeling observed ring-width data at the same network of sites. The estimated parameter values covary in physical space, and their locations in multidimensional parameter space provide insight into the dominant climatic controls on modeled tree-ring growth at each site as well as the stability of those controls. The estimation procedure is useful for forward and inverse modeling studies using VS-Lite to quantify the full range of model uncertainty stemming from its parameterization.

Development of a Process Oriented Calibration Scheme for the HBV Hydrological Model

1991 ◽  
Vol 22 (1) ◽  
pp. 15-36 ◽  
Author(s):  
Joakim Harlin
Keyword(s):  
Hydrological Model ◽  
Optimal Parameter ◽  
Model Performance ◽  
Computer Time ◽  
Fine Tuning ◽  
Parameter Estimates ◽  
Calibration Period ◽  
Calibration Scheme ◽  
Process Oriented ◽  
Iteration Loop

A process oriented calibration scheme (POC), developed for the HBV hydrological model is presented. Twelve parameters were calibrated in two steps. Firstly, initial parameter estimates were made from recession analysis of observed runoff. Secondly, the parameters were calibrated individually in an iteration loop starting with the snow routine, over the soil routine and finally the runoff-response function. This was done by minimizing different objective functions for different parameters and only over subperiods where the parameters were active. Approximately three hundred and fifty objective function evaluations were needed to find the optimal parameter set, which resulted in a computer time of about 17 hours on a 386 processor PC for a ten-year calibration period. Experiments were also performed with fine tuning as well as direct search of the response surface, where the parameters were allowed to change simultaneously. A calibration period length of between two and six years was found sufficient to find optimal parameters in the test basins. The POC scheme yielded as good model performance as after a manual calibration.

scholarly journals Bayesian calibration of firn densification models

2020 ◽  
Vol 14 (9) ◽  
pp. 3017-3032
Author(s):  
Vincent Verjans ◽  
Amber A. Leeson ◽  
Christopher Nemeth ◽  
C. Max Stevens ◽  
Peter Kuipers Munneke ◽  
...  
Keyword(s):  
Optimal Parameter ◽  
Ice Sheet ◽  
Calibration Method ◽  
Parameter Estimates ◽  
Age Difference ◽  
Bayesian Calibration ◽  
Surface Elevation Change ◽  
Independent Observations ◽  
Ice Sheet Mass Balance ◽  
Parameter Values

Abstract. Firn densification modelling is key to understanding ice sheet mass balance, ice sheet surface elevation change, and the age difference between ice and the air in enclosed air bubbles. This has resulted in the development of many firn models, all relying to a certain degree on parameter calibration against observed data. We present a novel Bayesian calibration method for these parameters and apply it to three existing firn models. Using an extensive dataset of firn cores from Greenland and Antarctica, we reach optimal parameter estimates applicable to both ice sheets. We then use these to simulate firn density and evaluate against independent observations. Our simulations show a significant decrease (24 % and 56 %) in observation–model discrepancy for two models and a smaller increase (15 %) for the third. As opposed to current methods, the Bayesian framework allows for robust uncertainty analysis related to parameter values. Based on our results, we review some inherent model assumptions and demonstrate how firn model choice and uncertainties in parameter values cause spread in key model outputs.

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