Some Observations Regarding the Statistical Determination of Stress Rupture Regression Lines

1979 ◽  
Vol 101 (4) ◽  
pp. 286-291
Author(s):  
P. P. Pizzo
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Stress Rupture ◽  
Anomalous Behavior ◽  
Creep Data ◽  
Statistical Determination ◽  
Selection Of

Observations concerning the statistical evaluation of creep data are presented. Methods currently employed in the determination of stress rupture regression lines can result in conflicting and necessarily invalid results. Anomalous behavior is principally associated with the selection of the dependent variable. However, it is the least squares method of curve fitting which introduces regression bias. Methods to improve the validity of least squares regressions are suggested.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

A Fourier Transform Infrared Study of Mineral Matter in Coal: The Application of a Least Squares Curve-Fitting Program

1981 ◽  
Vol 35 (1) ◽  
pp. 102-106 ◽  
Author(s):  
Paul C. Painter ◽  
Susan M. Rimmer ◽  
Randy W. Snyder ◽  
Alan Davis
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Curve Fitting ◽  
Fourier Transform Infrared ◽  
Mineral Matter ◽  
Infrared Study ◽  
Least Squares Curve Fitting ◽  
Mineral Mixtures ◽  
Good Agreement

The application of Fourier transform infrared spectroscopy to the quantitative determination of mineral matter in coal is discussed. The use of a least squares curve-fitting program allows a choice between standards to be made. The results of an analysis of mineral mixtures and a coal low temperature ash are presented. The results are in good agreement with known concentrations and those obtained by other methods of analysis.

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals Method of determining the distance to the object by analyzing its image blur

Vestnik MGSU ◽  
2015 ◽  
pp. 140-151 ◽  
Author(s):  
Aleksey Alekseevich Loktev ◽  
Daniil Alekseevich Loktev
Keyword(s):  
Least Squares ◽  
Statistical Approach ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Focal Length ◽  
Error Variance ◽  
Method Of Least Squares ◽  
Automated Control ◽  
Image Blur

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.

A least-squares method for the determination of the orientation matrix in single-crystal diffractometry

1970 ◽  
Vol 26 (2) ◽  
pp. 295-296 ◽  
Author(s):  
K. Tichý
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Reciprocal Vector ◽  
Orientation Matrix ◽  
The Matrix

An appropriate choice of the function minimized permits linearization of the least-squares determination of the matrix which transforms the diffraction indices into the components of the reciprocal vector in the diffractometer φ-axis system of coordinates. The coefficients of the least-squares equations are based on diffraction indices and measured diffractometer angles of three or more non-coplanar setting reflexions.

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