Analysis of errors in parameter estimation with application to physiological systems

1980 ◽  
Vol 239 (5) ◽  
pp. R390-R400
Author(s):  
T. M. Grove ◽  
G. A. Bekey ◽  
L. J. Haywood
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Measurement Errors ◽  
Estimation Error ◽  
Nonlinear Dynamic System ◽  
Parameter Estimates ◽  
Taylor Series Expansions ◽  
System Output ◽  
Model Equations ◽  
Physiological Systems

The accuracy of parameter estimation applied to physiological systems is analyzed. The method of analysis is applicable to procedures utilizing minimization of squared output error and a nonlinear dynamic system model. Three major sources of estimation error are described: 1) measurement error, 2) modeling error, and 3) optimization error. Measurement errors affect values used for the system output, the model input, and nonestimated parameters of the model. Modeling errors are due to failure to adequately describe the structure of the system and to numerical errors that occur in the digital computer solution of the model equations. Linearization by use of Taylor series expansions in the region of the nominal solution is used to obtain an expression for the covariance matrix of the parameter estimates in terms of the covariance matrix of each error source. The analysis is applied to the example of cardiac output estimation from respiratory measurements. The results demonstrate that an analysis of system identifiability is not sufficient to ensure usable estimates and that systematic error analysis is essential for assessing the usefulness of parameter estimation techniques.

scholarly journals SNP genotyping and parameter estimation in polyploids using low-coverage sequencing data

2017 ◽  
Author(s):  
Paul D. Blischak ◽  
Laura S. Kubatko ◽  
Andrea D. Wolfe
Keyword(s):  
Parameter Estimation ◽  
High Throughput Sequencing ◽  
Estimation Error ◽  
Parameter Estimates ◽  
Data Sets ◽  
Mixed Mating ◽  
Sequencing Data ◽  
Ploidy Levels ◽  
Sequencing Coverage ◽  
High Throughput Sequencing Data

AbstractMotivation:Genotyping and parameter estimation using high throughput sequencing data are everyday tasks for population geneticists, but methods developed for diploids are typically not applicable to polyploid taxa. This is due to their duplicated chromosomes, as well as the complex patterns of allelic exchange that often accompany whole genome duplication (WGD) events. For WGDs within a single lineage (auto polyploids), inbreeding can result from mixed mating and/or double reduction. For WGDs that involve hybridization (allopolyploids), alleles are typically inherited through independently segregating subgenomes.Results:We present two new models for estimating genotypes and population genetic parameters from genotype likelihoods for auto- and allopolyploids. We then use simulations to compare these models to existing approaches at varying depths of sequencing coverage and ploidy levels. These simulations show that our models typically have lower levels of estimation error for genotype and parameter estimates, especially when sequencing coverage is low. Finally, we also apply these models to two empirical data sets from the literature. Overall, we show that the use of genotype likelihoods to model non-standard inheritance patterns is a promising approach for conducting population genomic inferences in polyploids.Availability:A C++ program, EBG, is provided to perform inference using the models we describe. It is available under the GNU GPLv3 on GitHub:https://github.com/pblischak/polyploid-genotyping.Contact: [email protected].

SVD-TLD Sensing Algorithm for EES-MIMO Radar

2014 ◽  
Vol 1006-1007 ◽  
pp. 815-820
Author(s):  
Zhen Wang ◽  
Lan Xiang Zhu ◽  
Feng Yu ◽  
Lei Gu
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Cross Correlation ◽  
Estimation Error ◽  
Error Function ◽  
Mimo Radar ◽  
Ar Model ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
The Cross

Based on Electromagnetic Environmental Sensory(EES)and Multiple-input Multiple-Out(MIMO) radar sensing algorithm , this paper presents SVD-TLD perception algorithm, which firstly use the cross-spectrum AR model parameter estimation, and secondly considering the cross-correlation matrix of the estimation error function disturbance and lastly taking into account of the two ends of the equation, using the cross-correlation function of the estimated measurement errors to affect the Total Least Squares (TLS) method . Compared with the AR model parameter estimation, the accuracy of SVD algorithm cross-spectral estimation has significantly improved, greatly reducing the amount of computation and is more conducive to real-time online computing.

Optimal Position Estimate from a Stars Fix with Correlated Errors

1992 ◽  
Vol 45 (1) ◽  
pp. 126-133
Author(s):  
C. de Wit
Keyword(s):  
Covariance Matrix ◽  
Measurement Errors ◽  
Estimation Error ◽  
Systematic Errors ◽  
Position Error ◽  
Correlated Errors ◽  
Optimal Position ◽  
Position Estimate ◽  
Equal Contribution

This paper concerns the estimate of a ship's position from a sequence of measurements of 3, 4 or 5 altitudes of stars or planets. The measurement errors are assumed to be mutually correlated. This correlation is mainly caused by the appearance of so-called systematic errors. It is the main intention of this paper to dispense with the policy of pre-separation of these systematic errors. Instead, the equal contribution of some partial errors to the total measuring errors is fully accounted for by the formation of the covariance matrix, which corresponds with the vector of measurement errors. The algorithm produces a position estimate with a bias-free estimation error, meaning that the estimate and the error are stochastically independent. The resulting covariance matrix of the position error has a minimal trace.

NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS

2004 ◽  
Vol 14 (06) ◽  
pp. 1905-1933 ◽  
Author(s):  
HENNING U. VOSS ◽  
JENS TIMMER ◽  
JÜRGEN KURTHS
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Recursive Estimation ◽  
Cost Functions ◽  
Parameter Estimates ◽  
Nonlinear Dynamical ◽  
Estimation Techniques ◽  
The Cost

We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.

scholarly journals Numerical study of the evaporation process and parameter estimation analysis of an evaporation experiment

2009 ◽  
Vol 6 (6) ◽  
pp. 7385-7427
Author(s):  
K. Schneider-Zapp ◽  
O. Ippisch ◽  
K. Roth
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Hydraulic Properties ◽  
Numerical Study ◽  
Response Surfaces ◽  
Parameter Estimates ◽  
Physical Analysis ◽  
Potential Measurement ◽  
Soil Atmosphere ◽  
Experimental Findings

Abstract. Evaporation is an important process in soil-atmosphere interaction. The determination of hydraulic properties is one of the crucial parts in the simulation of water transport in porous media. Schneider et al. (2006) developed a new evaporation method to improve the estimation of hydraulic properties in the dry range. In this study we used numerical simulations of the experiment to study the physical dynamics in more detail, to optimise the boundary conditions and to choose the optimal combination of measurements. The physical analysis exposed, in accordance to experimental findings in the literature, two different evaporation regimes, a soil-atmosphere boundary layer dominated regime (regime I) in the saturated region and a hydraulically dominated regime (regime II). During this second regime a drying front forms which penetrates deeper into the soil as time passes. The sensitivity analysis showed that the result is especially sensitive at the transition between the two regimes. By using boundary condition changes it is possible to force the system to switch between the two regimes, e.g. from II back to I. Based on this findings a multistep experiment was developed. The response surfaces for all parameter combinations are flat and have a unique, localised minimum. Best parameter estimates are obtained if the evaporation flux and a potential measurement in 2 cm depth are used as target variables. Parameter estimation from simulated experiments with realistic measurement errors with a two-stage Monte-Carlo Levenberg-Marquardt procedure and manual rejection of obvious misfits lead to acceptable results for three different soil textures.

scholarly journals How meaningful are parameter estimates from models of inter-temporal choice?

2020 ◽  
Author(s):  
Timothy Ballard ◽  
Ashley Luckman ◽  
Emmanouil Konstantinidis
Keyword(s):  
Parameter Estimation ◽  
Choice Model ◽  
Estimation Error ◽  
Choice Models ◽  
Experimental Designs ◽  
Parameter Estimates ◽  
Choice Process ◽  
Parameter Recovery ◽  
Model Parameter ◽  
Latent Components

Decades of work has been dedicated to developing and testing models that characterize how people make inter-temporal choices. Although parameter estimates from these models are often interpreted as indices of latent components of the choice process, little work has been done to examine their reliability. This is problematic, because estimation error can bias conclusions that are drawn from these parameter estimates. We examine the reliability of inter-temporal choice model parameter estimates by conducting a parameter recovery analysis of 11 prominent models. We find that the reliability of parameter estimation varies considerably between models and the experimental designs upon which parameter estimates are based. We conclude that many parameter estimates reported in previous research are likely unreliable and provide recommendations on how to enhance reliability for those wishing to use inter-temporal choice models for measurement purposes.

scholarly journals Numerical study of the evaporation process and parameter estimation analysis of an evaporation experiment

2010 ◽  
Vol 14 (5) ◽  
pp. 765-781 ◽  
Author(s):  
K. Schneider-Zapp ◽  
O. Ippisch ◽  
K. Roth
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Measurement Errors ◽  
Hydraulic Properties ◽  
Numerical Study ◽  
Response Surfaces ◽  
Parameter Estimates ◽  
Physical Analysis ◽  
Potential Measurement ◽  
Soil Atmosphere

Abstract. Evaporation is an important process in soil-atmosphere interaction. The determination of hydraulic properties is one of the crucial parts in the simulation of water transport in porous media. Schneider et al. (2006) developed a new evaporation method to improve the estimation of hydraulic properties in the dry range. In this study we used numerical simulations of the experiment to study the physical dynamics in more detail, to optimise the boundary conditions and to choose the optimal combination of measurements. The physical analysis exposed, in accordance to experimental findings in the literature, two different evaporation regimes: (i) a soil-atmosphere boundary layer dominated regime (regime I) close to saturation and (ii) a hydraulically dominated regime (regime II). During this second regime a drying front (interface between unsaturated and dry zone with very steep gradients) forms which penetrates deeper into the soil as time passes. The sensitivity analysis showed that the result is especially sensitive at the transition between the two regimes. By changing the boundary conditions it is possible to force the system to switch between the two regimes, e.g. from II back to I. Based on this findings a multistep experiment was developed. The response surfaces for all parameter combinations are flat and have a unique, localised minimum. Best parameter estimates are obtained if the evaporation flux and a potential measurement in 2 cm depth are used as target variables. Parameter estimation from simulated experiments with realistic measurement errors with a two-stage Monte-Carlo Levenberg-Marquardt procedure and manual rejection of obvious misfits lead to acceptable results for three different soil textures.

scholarly journals Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical Development

2001 ◽  
Vol 5 (2) ◽  
pp. 215-223 ◽  
Author(s):  
E. Todini
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Theoretical Development ◽  
Comprehensive Treatment ◽  
Parameter Estimates ◽  
Wide Field ◽  
Estimation Uncertainty ◽  
Parameter Estimation Uncertainty ◽  
Variance Covariance Matrix

Abstract. This paper deals with a theoretical approach to assessing the effects of parameter estimation uncertainty both on Kriging estimates and on their estimated error variance. Although a comprehensive treatment of parameter estimation uncertainty is covered by full Bayesian Kriging at the cost of extensive numerical integration, the proposed approach has a wide field of application, given its relative simplicity. The approach is based upon a truncated Taylor expansion approximation and, within the limits of the proposed approximation, the conventional Kriging estimates are shown to be biased for all variograms, the bias depending upon the second order derivatives with respect to the parameters times the variance-covariance matrix of the parameter estimates. A new Maximum Likelihood (ML) estimator for semi-variogram parameters in ordinary Kriging, based upon the assumption of a multi-normal distribution of the Kriging cross-validation errors, is introduced as a mean for the estimation of the parameter variance-covariance matrix. Keywords: Kriging, maximum likelihood, parameter estimation, uncertainty

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