Determination of the Exact Confidence Intervals for Parameters in a Model of Direct Measurements With Independent Random Errors

2021 ◽  
Author(s):  
Gejza Wimmer ◽  
Viktor Witkovsky
Keyword(s):  
Confidence Intervals ◽  
Random Errors ◽  
Direct Measurements ◽  
Exact Confidence Intervals

Statistics and parallaxes

1978 ◽  
Vol 48 ◽  
pp. 7-29
Author(s):  
T. E. Lutz
Keyword(s):  
Experimental Design ◽  
Statistical Methods ◽  
Review Paper ◽  
Systematic Errors ◽  
Past Experience ◽  
Random Errors ◽  
Trigonometric Parallaxes ◽  
Systematic And Random Errors

This review paper deals with the use of statistical methods to evaluate systematic and random errors associated with trigonometric parallaxes. First, systematic errors which arise when using trigonometric parallaxes to calibrate luminosity systems are discussed. Next, determination of the external errors of parallax measurement are reviewed. Observatory corrections are discussed. Schilt’s point, that as the causes of these systematic differences between observatories are not known the computed corrections can not be applied appropriately, is emphasized. However, modern parallax work is sufficiently accurate that it is necessary to determine observatory corrections if full use is to be made of the potential precision of the data. To this end, it is suggested that a prior experimental design is required. Past experience has shown that accidental overlap of observing programs will not suffice to determine observatory corrections which are meaningful.

Corrosion Metal Loss Interaction From In-Line Inspection and How it Can Affect the Calculated Failure Pressure

2012 ◽  
Author(s):  
Lucinda Smart ◽  
Richard McNealy ◽  
Harvey Haines
Keyword(s):  
Field Measurements ◽  
Metal Loss ◽  
Data Correlation ◽  
Failure Pressure ◽  
Industry Standards ◽  
Direct Measurements ◽  
Non Destructive ◽  
Flux Leakage

In-Line Inspection (ILI) is used to prioritize metal loss conditions based on predicted failure pressure in accordance with methods prescribed in industry standards such as ASME B31G-2009. Corrosion may occur in multiple areas of metal loss that interact and may result in a lower failure pressure than if flaws were analyzed separately. The B31G standard recommends a flaw interaction criterion for ILI metal loss predictions within a longitudinal and circumferential spacing of 3 times wall thickness, but cautions that methods employed for clustering of ILI anomalies should be validated with results from direct measurements in the ditch. Recent advances in non-destructive examination (NDE) and data correlation software have enabled reliable comparisons of ILI burst pressure predictions with the results from in-ditch examination. Data correlation using pattern matching algorithms allows the consideration of detection and reporting thresholds for both ILI and field measurements, and determination of error in the calculated failure pressure prediction attributable to the flaw interaction criterion. This paper presents a case study of magnetic flux leakage ILI failure pressure predictions compared with field results obtained during excavations. The effect of interaction criterion on calculated failure pressure and the probability of an ILI measurement underestimating failure pressure have been studied. We concluded a reason failure pressure specifications do not exist for ILI measurements is because of the variety of possible interaction criteria and data thresholds that can be employed, and demonstrate herein a method for their validation.

Median based algorithm for sub-pixel estimation of extrema positions of diffuse light reflection signal

2021 ◽  
Vol 2021 (49) ◽  
pp. 37-44
Author(s):  
I. B. Ivasiv ◽  
Keyword(s):  
Linear Array ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Diffuse Light ◽  
Random Errors ◽  
Centroid Algorithm ◽  
Piecewise Linear Interpolation ◽  
Light Reflectance ◽  
Cumulative Function

It has been proposed to utilize the median algorithm for determination of the extrema positions of diffuse light reflectance intensity distribution by a discrete signal of a photodiode linear array. The algorithm formula has been deduced on the base of piecewise-linear interpolation for signal representation by cumulative function. It has been shown that this formula is much simpler for implementation than known centroid algorithm and the noise immune Blais and Rioux detector algorithm. Also, the methodical systematic errors for zero noise as well as the random errors for full common mode additive noises and uncorrelated noises have been estimated and compared for mentioned algorithms. In these terms, the proposed median algorithm is proportionate to Blais and Rioux algorithm and considerably better then centroid algorithm.

Combined ventilatory and breath-holding evaluation of sensitivity to respiratory gases

1959 ◽  
Vol 14 (3) ◽  
pp. 353-356 ◽  
Author(s):  
Robert C. Stroud
Keyword(s):  
Carbon Dioxide ◽  
Ventilatory Response ◽  
Direct Determination ◽  
Breath Holding ◽  
Respiratory Response ◽  
Data Comparison ◽  
Direct Measurements ◽  
Respiratory Gases ◽  
Definite Role

Direct measurements of the ventilatory response to variations in CO2 tension independent of changes in O2 tension are easily obtained by breathing mixtures of carbon dioxide in 100% oxygen. Direct determination of the respiratory response to O2, however, is not possible due to alternations in CO2 tension resulting from changes in ventilation. Therefore, an attempt has been made to determine this response empirically by a combined analysis of breath-holding and ventilatory data. Comparison of experimentally determined responses to various combinations of O2 and CO2 tensions agree quite well with those predicted by this approach and indicate that oxygen plays a small but definite role in the regulation of eupnic breathing at sea level. Submitted on October 22, 1958

scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

Accurate Determination of Object Position from Imprecise Data

1998 ◽  
Vol 120 (4) ◽  
pp. 559-564 ◽  
Author(s):  
K. C. Gupta ◽  
P. Chutakanonta
Keyword(s):  
Accurate Determination ◽  
Measurement Data ◽  
Decomposition Methods ◽  
Basic Method ◽  
Random Errors ◽  
Object Position ◽  
Cad Cam ◽  
Simulator Design ◽  
Vehicle Simulator

The problem of accurate determination of object position from imprecise and excess measurement data arises in kinematics, biomechanics, robotics, CAD/CAM and flight/vehicle simulator design. Several methods described in the literature are reviewed. Two new methods which take advantage of the modern matrix oriented software (e.g., MATLAB, IMSL, EISPACK) are presented and compared with a “basic” method. It is found that both of the proposed decomposition methods (I: SVD/QR and II: SVD/QS) give better absolute results than a “basic” method available from the text books. On a relative basis, the second method (SVD/QS Decomposition) gives slightly better results than the first method (SVD/QR Decomposition). Examples are presented for the cases when the points chosen are nearly dependent and when the independent points have small random errors in their coordinates.

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