scholarly journals Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Ahmed Ramadan ◽  
Connor Boss ◽  
Jongeun Choi ◽  
N. Peter Reeves ◽  
Jacek Cholewicki ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Human Subjects ◽  
Information Matrix ◽  
Computation Time ◽  
Model Complexity ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Lasso Method ◽  
Sensitive Parameters

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

scholarly journals Stochastic Modeling of Rainfall in Peninsular Malaysia Using Bartlett Lewis Rectangular Pulses Models

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Ibrahim Suliman Hanaish ◽  
Kamarulzaman Ibrahim ◽  
Abdul Aziz Jemain
Keyword(s):  
Objective Function ◽  
Goodness Of Fit ◽  
Optimization Technique ◽  
Generalized Method Of Moments ◽  
Rain Gauge ◽  
Peninsular Malaysia ◽  
Weight Functions ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Hourly Rainfall

Three versions of Bartlett Lewis rectangular pulse rainfall models, namely, the Original Bartlett Lewis (OBL), Modified Bartlett Lewis (MBL), and 2N-cell-type Bartlett Lewis model (BL2n), are considered. These models are fitted to the hourly rainfall data from 1970 to 2008 obtained from Petaling Jaya rain gauge station, located in Peninsular Malaysia. The generalized method of moments is used to estimate the model parameters. Under this method, minimization of two different objective functions which involve different weight functions, one weight is inversely proportional to the variance and another one is inversely proportional to the mean squared, is carried out using Nelder-Mead optimization technique. For the purpose of comparison of the performance of the three different models, the results found for the months of July and November are used for illustration. This performance is assessed based on the goodness of fit of the models. In addition, the sensitivity of the parameter estimates to the choice of the objective function is also investigated. It is found thatBL2nslightly outperformsOBL. However, the best model is the Modified Bartlett LewisMBL, particularly when the objective function considered involves weight which is inversely proportional to the variance.

Practical identifiability of model parameters by combined respirometric-titrimetric measurements

2001 ◽  
Vol 43 (7) ◽  
pp. 347-355 ◽  
Author(s):  
B. Petersen ◽  
K. Gernaey ◽  
P. A. Vanrolleghem
Keyword(s):  
Fisher Information Matrix ◽  
Information Matrix ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Concentration Data ◽  
Sensitivity Functions ◽  
Practical Identifiability ◽  
Lower Accuracy ◽  
Accuracy Parameter

An earlier study on theoretical identifiability of parameters for a two-step nitrification model showed that a unique estimation of the yield YA1 is possible with combined respirometric-titrimetric data, contrary to the case where only one type of measurement is available. Here, the practical identifiability of model parameters was investigated via evaluation of the output sensitivity functions and the corresponding Fisher Information Matrix (FIM). It appeared that the FIM was not sufficiently powerful to predict the practical identifiability of this case with combined measurements as parameters could indeed be identified despite the fact that the FIM became singular. The accuracy of parameter estimates based on respirometric and titrimetric data and combination thereof was also investigated. Estimation on titrimetric data (Hp) was very accurate and a fast convergence of the objective function towards a minimum was obtained. The latter also holds for estimation on oxygen uptake rate data (rO), however with a lower accuracy. Parameter estimation based on oxygen concentration data (SO) was more complex but resulted in a higher accuracy. Thus, when the highest accuracy is needed it is recommended to estimate parameters initially on Hp and/or rO data, and to subsequently use these parameters as initial values for final, and more accurate estimation on SO data.

scholarly journals Fitting a logistic growth model to yield traits of lettuce cultivars growing in summer

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Fernanda Carini ◽  
Alberto Cargnelutti-Filho ◽  
Jéssica Maronez De Souza ◽  
Rafael Vieira Pezzini ◽  
Cassiane Ubessi ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Growth Model ◽  
Iterative Process ◽  
Logistic Model ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Logistic Growth ◽  
Model Parameters ◽  
Yield Traits ◽  
Logistic Growth Model

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.

Simultaneous structure and parameter identification of multivariate systems by matrix decomposition

2016 ◽  
Vol 38 (12) ◽  
pp. 1411-1420 ◽  
Author(s):  
Benben Jiang ◽  
Fan Yang ◽  
Dexian Huang
Keyword(s):  
Parameter Identification ◽  
Structure Determination ◽  
Information Matrix ◽  
Matrix Decomposition ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Structure ◽  
Multiple Model ◽  
Process Data ◽  
Multivariate Systems

Structure determination and parameter identification of multivariate systems are crucial but rather difficult issues in system identification. Due to the explosive growth of process data along with the scale increase of industrial processes, directional links between variables of such complex processes are often undistinguishable, which is indispensable to model structure determination but is often assumed to be known beforehand in most identification methods. In this article, a new modelling approach is developed to simultaneously estimate the model parameters and structures (including model orders as well as the directional links between different process variables) of multivariate systems. A vector auto-regressive (VAR) form is utilized as the model formulation in this algorithm. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the VAR representation. Then by utilizing the upper diagonal factorization, all the parameter estimates of all path models with orders from zero to m, as well as the corresponding cost function values, can be obtained simultaneously. The effectiveness of the proposed method is demonstrated via a numerical example and a distillation column system.

scholarly journals Event-scale power law recession analysis: Quantifying methodological uncertainty

2016 ◽  
Author(s):  
David N. Dralle ◽  
Nathaniel J. Karst ◽  
Kyriakos Charalampous ◽  
Sally E. Thompson
Keyword(s):  
Impact Parameter ◽  
Power Law ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Event Scale ◽  
Methodological Choices ◽  
Daily Streamflow ◽  
Streamflow Data

Abstract. The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power-law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely-used power-law recession model. We show that: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness-of-fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship between the power law recession scale parameter and catchment antecedent wetness varies depending on recession definition and fitting choices.

Multiple-objective criteria for optimal experimental design: application to ferrokinetics

1985 ◽  
Vol 248 (3) ◽  
pp. R378-R386 ◽  
Author(s):  
M. H. Nathanson ◽  
G. M. Saidel
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Objective Function ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Multiple Objective ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Conditions ◽  
New Criterion

Optimal experimental design is used to predict the experimental conditions that will allow the "best" estimates of model parameters. A variety of criteria must be considered before an optimal design is chosen. Maximizing the determinant of the information matrix (D optimality), which tends to produce the most precise simultaneous estimates of all parameters, is commonly considered as the primary criterion. To complement this criterion, we present another whose effect is to reduce the interaction among the parameter estimates so that changes in any one parameter can be more distinct. This new criterion consists of maximizing the determinant of an appropriately scaled information matrix (M optimality). These criteria are applied jointly in a multiple-objective function. To illustrate the use of these concepts, we develop an optimal experimental design of blood sampling schedules using a detailed ferrokinetic model.

scholarly journals Assessment of Homodyned K Distribution Modeling Ultrasonic Speckles from Scatterers with Varying Spatial Organizations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xiao Hu ◽  
Yufeng Zhang ◽  
Li Deng ◽  
Guanghui Cai ◽  
Qinghui Zhang ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Human Subjects ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Practical Applications ◽  
Distribution Modeling ◽  
Gamma Distributions ◽  
Carotid Arterial

Objective. This paper presents an assessment of physical meanings of parameter and goodness of fit for homodyned K (HK) distribution modeling ultrasonic speckles from scatterer distributions with wide-varying spatial organizations. Methods. A set of 3D scatterer phantoms based on gamma distributions is built to be implemented from the clustered to random to uniform scatterer distributions continuously. The model parameters are obtained by maximum likelihood estimation (MLE) from statistical histograms of the ultrasonic envelope data and then compared with those by the optimally fitting models chosen from three single distributions. Results show that the parameters of the HK distribution still present their respective physical meanings of independent contributions in the scatterer distributions. Moreover, the HK distribution presents better goodness of fit with a maximum relative MLE difference of 6.23% for random or clustered scatterers with a well-organized periodic structure. Experiments based on ultrasonic envelope data from common carotid arterial B-mode images of human subjects validate the modeling performance of HK distribution. Conclusion. We conclude that the HK model for ultrasonic speckles is a better choice for characterizing tissue with a wide variety of spatial organizations, especially the emphasis on the goodness of fit for the tissue in practical applications.

scholarly journals Use of Bayesian Methods to Improve Prediction of Panicle and Shoot Blight Severity of Pistachio in California

2006 ◽  
Vol 96 (10) ◽  
pp. 1142-1147 ◽  
Author(s):  
Asimina L. Mila ◽  
Themis J. Michailides
Keyword(s):  
Bayesian Analysis ◽  
Confidence Intervals ◽  
Disease Severity ◽  
Bayesian Methods ◽  
Drip Irrigation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Leaf Infection ◽  
Shoot Blight ◽  
Rainy Days

Panicle and shoot blight, caused by a Fusicoccum sp., is one of the major aboveground diseases of pistachio in California. The effects of temperature, number of continuous rainy days in April and May, irrigation system, and incidence of latent infection of the Fusicoccum sp. on severity of panicle and shoot blight of pistachio leaves and fruit have been quantified previously, using data collected from 1999 through 2001. A predictive model for leaves and another model for fruit with good explanatory power were generated. In 2003 and 2004, newly collected data were used to evaluate the two models with non-Bayesian and Bayesian methods. The 95% credible (i.e., confidence) intervals of initial (before modification with non-Bayesian and Bayesian methods) and updated parameter estimates were used to investigate their prognostic validity. In 2003, the non-Bayesian analysis resulted in all parameter estimates, with the exception of cumulative daily mean temperature from 1 June until harvest, having different 95% confidence intervals than the parameter estimates of the original models. In addition, the parameter estimates for drip irrigation for the leaf infection and the parameter estimates for drip irrigation and number of continuous rainy days in April and May for fruit infection were not statistically significant. With Bayesian methods, the reestimated model parameters had overlapping 95% credible intervals with the initial estimated parameters, except for the number of continuous rainy days in April and May. When the two sets of modified parameter estimates were used to predict disease severity, statistically significant (α = 0.05) differences between observed and predicted disease severities were found with non-Bayesian analysis for leaf infection in three locations and with Bayesian analysis for fruit infection in one orchard. The parameter estimates were modified again at the end of the 2004 season and were all statistically significant with both non-Bayesian and Bayesian methods. Both sets of parameter estimates gave predictions that were not significantly different from observed disease severity on leaves and fruit in all monitored orchards in 2004. In summary, Bayesian methods gave more consistent results when used to update parameter estimates with new information and yielded predictions not statistically different from observed disease severity in more cases than the non-Bayesian analysis.

Evaluation of the information content of long-term wastewater characteristics data in relation to activated sludge model parameters

2017 ◽  
Vol 75 (6) ◽  
pp. 1370-1389 ◽  
Author(s):  
Jamal Alikhani ◽  
Imre Takacs ◽  
Ahmed Al-Omari ◽  
Sudhir Murthy ◽  
Arash Massoudieh
Keyword(s):  
Activated Sludge ◽  
Hybrid Genetic Algorithm ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Main Role ◽  
Activated Sludge Model ◽  
Parameter Estimations ◽  
Reliable Parameter ◽  
Denitrification Bioreactor ◽  
Sensitive Parameters

A parameter estimation framework was used to evaluate the ability of observed data from a full-scale nitrification–denitrification bioreactor to reduce the uncertainty associated with the bio-kinetic and stoichiometric parameters of an activated sludge model (ASM). Samples collected over a period of 150 days from the effluent as well as from the reactor tanks were used. A hybrid genetic algorithm and Bayesian inference were used to perform deterministic and parameter estimations, respectively. The main goal was to assess the ability of the data to obtain reliable parameter estimates for a modified version of the ASM. The modified ASM model includes methylotrophic processes which play the main role in methanol-fed denitrification. Sensitivity analysis was also used to explain the ability of the data to provide information about each of the parameters. The results showed that the uncertainty in the estimates of the most sensitive parameters (including growth rate, decay rate, and yield coefficients) decreased with respect to the prior information.

A Note on Confidence Intervals and Model Specification

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 33-42
Author(s):  
Thomas Otter
Keyword(s):  
Confidence Intervals ◽  
Generalized Linear Model ◽  
Statistical Information ◽  
Regression Coefficients ◽  
Model Specification ◽  
Model Parameters ◽  
Exploratory Research ◽  
Empirical Calibration ◽  
Credible Intervals ◽  
Model Structures

Empirical research in marketing often is, at least in parts, exploratory. The goal of exploratory research, by definition, extends beyond the empirical calibration of parameters in well established models and includes the empirical assessment of different model specifications. In this context researchers often rely on the statistical information about parameters in a given model to learn about likely model structures. An example is the search for the 'true' set of covariates in a regression model based on confidence intervals of regression coefficients. The purpose of this paper is to illustrate and compare different measures of statistical information about model parameters in the context of a generalized linear model: classical confidence intervals, bootstrapped confidence intervals, and Bayesian posterior credible intervals from a model that adapts its dimensionality as a function of the information in the data. I find that inference from the adaptive Bayesian model dominates that based on classical and bootstrapped intervals in a given model.

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