scholarly journals Evaluation of linear regression techniques for atmospheric applications: The importance of appropriate weighting

2017 ◽  
Author(s):  
Cheng Wu ◽  
Jian Zhen Yu
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Measurement Uncertainty ◽  
Measurement Errors ◽  
Linear Measurement ◽  
Least Square ◽  
Pseudorandom Number Generator ◽  
Comparison Results ◽  
Deming Regression ◽  
Regression Techniques

Abstract. Linear regression techniques are widely used in atmospheric science, but are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The regression techniques tested are Ordinary Least Square (OLS), Deming Regression (DR), Orthogonal Distance Regression (ODR), Weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne Twister (MT) pseudorandom number generator. The numerical simulations are also improved by: (a) refining the parameterization of non-linear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found an improper λ in DR can leads to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. With the knowledge of an appropriate weighting, DR, WODR and YR are recommended for atmospheric studies when both x and y data have measurement errors.

scholarly journals Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

2018 ◽  
Vol 11 (2) ◽  
pp. 1233-1250 ◽  
Author(s):  
Cheng Wu ◽  
Jian Zhen Yu
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Measurement Uncertainty ◽  
Measurement Errors ◽  
Ordinary Least Squares ◽  
Pseudorandom Number Generator ◽  
Data Generation ◽  
Comparison Results ◽  
Deming Regression ◽  
Regression Techniques

Abstract. Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

Optimal Weighted Least Square Data Fusion Method for Redundant IMU Based on Calculation of Measurement Error

2012 ◽  
Vol 241-244 ◽  
pp. 149-155
Author(s):  
Chuan Xing ◽  
Hai Zhang
Keyword(s):  
Measurement Error ◽  
Data Fusion ◽  
Measurement Errors ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square ◽  
Weighted Matrix ◽  
Measurement Results ◽  
The Difference ◽  
Projection Error

A dodecahedron non-orthogonal redundant IMU configuration was selected as model. To improve fusion accuracy, we proposed an effective calculation method for measurement errors based on the correlation between measurement errors and fusion errors. The method considered the difference between traditional data fusion vector’s projection and measurement results, and then made a conversion from projection error to measurement error. Combined with optimal weighted least square method, measurement error was used to generate an optimal weighted matrix, and this made data fusion errors minimum. Simulations also proved that the fusion result of this method is more accurate than the result of traditional method.

Analysis of the random measurement error of areal 3D coordinate measurements exclusively based on measurement repetitions

2021 ◽  
Vol 88 (2) ◽  
pp. 71-77
Author(s):  
Andreas Michael Müller ◽  
Tino Hausotte
Keyword(s):  
Measurement Error ◽  
Measurement Uncertainty ◽  
Measurement System ◽  
Measurement Errors ◽  
Random Measurement Error ◽  
Additional Information ◽  
Random Measurement ◽  
Random Components ◽  
Measurement Object ◽  
X Ray Computed

Abstract The measurement uncertainty characteristics of a measurement system are an important parameter when evaluating the suitability of a certain measurement system for a specific measurement task. The measurement uncertainty can be calculated from observed measurement errors, which consist of both systematic and random components. While the unfavourable influence of systematic components can be compensated by calibration, random components are inherently not correctable. There are various measurement principles which are affected by different measurement error characteristics depending on specific properties of the measurement task, e. g. the optical surface properties of the measurement object when using fringe projection or the material properties when using industrial X-ray computed tomography. Thus, it can be helpful in certain scenarios if the spatial distribution of the acquisition quality as well as uncertainty characteristics on the captured surface of a certain measurement task can be found out. This article demonstrates a methodology to determine the random measurement error solely from a series of measurement repetitions without the need of additional information, e. g. a reference measurement or the nominal geometry of the examined part.

Predictive Distributions in the Presence of Measurement Errors

1996 ◽  
Vol 10 (4) ◽  
pp. 601-611 ◽  
Author(s):  
Irwin Guttman ◽  
Ulrich Menzefricke
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Gibbs Sampler ◽  
Linear Regression Model ◽  
Measurement Errors ◽  
Predictive Distribution ◽  
Multivariate Normal ◽  
Prior Distributions ◽  
True Value ◽  
Regression Parameters

We consider a hierarchical linear regression model where the regression parameters for the units have a multivariate normal distribution whose parameters are unknown. Several replications are available for each unit. The design matrices for the units need not be the same. A complicating feature of the model is that each observation is subject to measurement error. The objective of the paper is to derive the predictive distribution of the “true” value of the response at a given design point. A Bayesian treatment is given to the problem. In addition to standard prior distributions, other prior distributions are considered. The calculations are done with the Gibbs sampler. An example is discussed in detail.

scholarly journals Axial variation in flexural stiffness of plant stem segments: measurement methods and the influence of measurement uncertainty

Plant Methods ◽  
2021 ◽  
Vol 17 (1) ◽  
Author(s):  
Nathanael Martin-Nelson ◽  
Brandon Sutherland ◽  
Michael Yancey ◽  
Chung Shan Liao ◽  
Christopher J. Stubbs ◽  
...  
Keyword(s):  
Measurement Error ◽  
Measurement Uncertainty ◽  
Measurement Errors ◽  
Flexural Stiffness ◽  
System Of Equations ◽  
Physical Test ◽  
Axial Variation ◽  
Plant Stem ◽  
Flexural Tests ◽  
Stem Segments

Abstract Background Flexural three-point bending tests are useful for characterizing the mechanical properties of plant stems. These tests can be performed with minimal sample preparation, thus allowing tests to be performed relatively quickly. The best-practice for such tests involves long spans with supports and load placed at nodes. This approach typically provides only one flexural stiffness measurement per specimen. However, by combining flexural tests with analytic equations, it is possible to solve for the mechanical characteristics of individual stem segments. Results A method is presented for using flexural tests to obtain estimates of flexural stiffness of individual segments. This method pairs physical test data with analytic models to obtain a system of equations. The solution of this system of equations provides values of flexural stiffness for individual stalk segments. Uncertainty in the solved values for flexural stiffness were found to be strongly dependent upon measurement errors. Row-wise scaling of the system of equations reduced the influence of measurement error. Of many possible test combinations, the most advantageous set of tests for performing these measurements were identified. Relationships between measurement uncertainty and solution uncertainty were provided for two different testing methods. Conclusions The methods presented in this paper can be used to measure the axial variation in flexural stiffness of plant stem segments. However, care must be taken to account for the influence of measurement error as the individual segment method amplifies measurement error. An alternative method involving aggregate flexural stiffness values does not amplify measurement error, but provides lower spatial resolution.

PENGARUH KNOWLEDGE MANAGEMENT, KOMPETENSI, MOTIVASI TERHADAP KINERJA KARYAWAN

2015 ◽  
Vol 5 (2) ◽  
pp. 1
Author(s):  
Miftahol Arifin
Keyword(s):  
Knowledge Management ◽  
Linear Regression ◽  
Significant Influence ◽  
Employee Performance ◽  
Least Square Method ◽  
Least Square ◽  
Analysis Tool ◽  
Ordinary Least Square ◽  
Competence Motivation ◽  
Performance Analyze

The purpose of this research is to analyze the influence of knowledge management on employee performance, analyze the effect of competence on employee performance, analyze the influence of motivation on employee performance). In this study, samples taken are structural employees PT.centris Kingdom Taxi Yogyakarta. The analysis tool in this study using multiple linear regression with Ordinary Least Square method (OLS). The conclusion of this study showed that the variables of knowledge management has a significant influence on employee performance, competence variables have an influence on employee performance, motivation variables have an influence on employee performance, The analysis showed that the variables of knowledge management, competence, motivation on employee performance.Keywords: knowledge management, competence, motivation, employee performance.

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

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