scholarly journals Growth of random errors in temperature forecasts by numerical method using centred time-differences

MAUSAM ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 15-22
Author(s):  
D Y P. RAO ◽  
K. S. RAMAMURTI
Keyword(s):  
Numerical Method ◽  
Random Error ◽  
Initial Level ◽  
One Dimension ◽  
Random Errors ◽  
Horizontal Advection ◽  
Grid Points ◽  
Forward Differences

The growth of initial random errors in temperature forecasts by numerical method using centred time-differenced is investigated. Horizontal advection in one dimension is considered. Assuming that there is no correlation between the initial random errors as the different grid points and neglecting any correlation that may develop in the col1rse of computation, the random errors grow much more rapidly in this method than in forward time differencing. In both methods, correlations develop between the random errors at different grid points in the course of computation. When these are taken in to account, the growth of random errors is further enhanced in the forward differences. In the centred time-differences method, these correlations keep the random error almost at the initial level.

On the Smoothing of Observed Data

1937 ◽  
Vol 33 (4) ◽  
pp. 444-450 ◽  
Author(s):  
Harold Jeffreys
Keyword(s):  
Standard Error ◽  
Random Error ◽  
Simple Function ◽  
Standard Errors ◽  
Random Errors ◽  
Previous Theory ◽  
Know How ◽  
True Value ◽  
Actual Error ◽  
Range Of Variation

1. It often happens that we have a series of observed data for different values of the argument and with known standard errors, and wish to remove the random errors as far as possible before interpolation. In many cases previous considerations suggest a form for the true value of the function; then the best method is to determine the adjustable parameters in this function by least squares. If the number required is not initially known, as for a polynomial where we do not know how many terms to retain, the number can be determined by finding out at what stage the introduction of a new parameter is not supported by the observations*. In many other cases, again, existing theory does not suggest a form for the solution, but the observations themselves suggest one when the departures from some simple function are found to be much less than the whole range of variation and to be consistent with the standard errors. The same method can then be used. There are, however, further cases where no simple function is suggested either by previous theory or by the data themselves. Even in these the presence of errors in the data is expected. If ε is the actual error of any observed value and σ the standard error, the expectation of Σε2/σ2 is equal to the number of observed values. Part, at least, of any irregularity in the data, such as is revealed by the divided differences, can therefore be attributed to random error, and we are entitled to try to reduce it.

scholarly journals Uses and limitations of statistical accounting for random error correlations, in the validation of dietary questionnaire assessments

2002 ◽  
Vol 5 (6a) ◽  
pp. 969-976 ◽  
Author(s):  
Rudolf Kaaks ◽  
Pietro Ferrari ◽  
Antonio Ciampi ◽  
Martyn Plummer ◽  
Elio Riboli
Keyword(s):  
Random Error ◽  
Statistical Models ◽  
Validation Studies ◽  
Dietary Assessment ◽  
Nutritional Epidemiology ◽  
Random Errors ◽  
Doubly Labelled Water ◽  
Dietary Assessment Methods ◽  
Simultaneous Comparisons ◽  
Replicate Measurements

AbstractObjective:To examine statistical models that account for correlation between random errors of different dietary assessment methods, in dietary validation studies.Setting:In nutritional epidemiology, sub-studies on the accuracy of the dietary questionnaire measurements are used to correct for biases in relative risk estimates induced by dietary assessment errors. Generally, such validation studies are based on the comparison of questionnaire measurements (Q) with food consumption records or 24-hour diet recalls (R). In recent years, the statistical analysis of such studies has been formalised more in terms of statistical models. This made the need of crucial model assumptions more explicit. One key assumption is that random errors must be uncorrelated between measurements Q and R, as well as between replicate measurements R1 and R2 within the same individual. These assumptions may not hold in practice, however. Therefore, more complex statistical models have been proposed to validate measurements Q by simultaneous comparisons with measurements R plus a biomarker M, accounting for correlations between the random errors of Q and R.Conclusions:The more complex models accounting for random error correlations may work only for validation studies that include markers of diet based on physiological knowledge about the quantitative recovery, e.g. in urine, of specific elements such as nitrogen or potassium, or stable isotopes administered to the study subjects (e.g. the doubly labelled water method for assessment of energy expenditure). This type of marker, however, eliminates the problem of correlation of random errors between Q and R by simply taking the place of R, thus rendering complex statistical models unnecessary.

Corrections to Equations for Estimating the Counting-Statistical Errors in Diffraction Stress Measurements

1995 ◽  
Vol 28 (5) ◽  
pp. 590-593 ◽  
Author(s):  
R. A. Winholtz
Keyword(s):  
Monte Carlo ◽  
Random Error ◽  
Monte Carlo Model ◽  
Conservative Estimate ◽  
Random Errors ◽  
Stress Measurements ◽  
Statistical Errors ◽  
Replicated Measurements

Two corrections are made to the equations for estimating the counting statistical errors in diffraction stress measurements. It is shown that the previous equations provide a conservative estimate of the counting-statistical component of the random errors in stress measurements. The results from the corrected equations are compared to a Monte Carlo model and to replicated measurements. A procedure to handle other sources of random error is also suggested.

Comparison of geometric uncertainties between alpha cradle and thermoplastic ray cast immobilisation in abdominopelvic radiotherapy: a prospective study

2011 ◽  
Vol 11 (4) ◽  
pp. 239-248 ◽  
Author(s):  
Saikat Das ◽  
Subhashini John ◽  
Paul Ravindran ◽  
Rajesh Isiah ◽  
Rajesh B ◽  
...  
Keyword(s):  
Random Error ◽  
Systematic Errors ◽  
Target Volume ◽  
Reference Image ◽  
Ratio Test ◽  
Setup Error ◽  
Random Errors ◽  
Geometric Uncertainties ◽  
The Difference ◽  
Portal Images

AbstractContext: Setup error significantly affects the accuracy of treatment and outcome in high precision radiotherapy.Aims: To determine total, systematic, random error and clinical target volume (CTV) to planning target volume (PTV) margin with alpha cradle (VL) and ray cast (RC) immobilisation in abdominopelvic region.Methods and material: Setup error was compared by using digitally reconstructed radiograph (DRR) as reference image with electronic portal image (EPI) taken during the treatment. Statistical analysis used: The total errors in mediolateral (ML), craniocaudal (CC) and anteroposterior (AP) directions were compared by t-test. For systematic and random errors variance ratio test (F-statistics) was used. Margins were calculated using International Commission of Radiation Units (ICRU), Stroom’s and van Herk’s formula.Results: A total number of 306 portal images were analysed with 144 images in RC group and 162 images in VL group. For VL, in ML, CC, AP directions systematic errors were, in cm, (0.45, 0.29, 0.41), random errors (0.48, 0.32, 0.58), CTV to PTV margins (1.24, 0.80, 1.25), respectively. For RC, systematic errors were (0.25, 0.37, 0.80), random error (0.46, 0.80, 0.33), CTV to PTV margins (0.82, 1.30, 1.08), respectively. The difference of random error in CC and AP directions were statistically significant.Conclusions: Geometric errors and CTV to PTV margins are different in different directions. For abdomen and pelvis in VL immobilisation, the margin ranged from 8 mm to 12.4 mm and for RC it was 8.2 mm to 13 mm. Therefore, a margin of 10 mm with online correction would be adequate.

Modeling Study on Random Error of Fiber Optic Gyro

2012 ◽  
Vol 239-240 ◽  
pp. 167-171
Author(s):  
Fan Zhang
Keyword(s):  
Random Walk ◽  
Random Error ◽  
Fiber Optic ◽  
Angular Rate ◽  
Measurement Unit ◽  
Random Errors ◽  
Fiber Optic Gyro ◽  
Zero Bias ◽  
Instability Rate ◽  
Bias Instability

An accurate modeling method for the random error of the fiber optic gyro (FOG) is presented. Taking the FOG in the inertial measurement unit of one specific inertial navigation system as the subject investigated, the method is composed of the data acquisition, preprocessing, establishing the FOG AR(2) model and performing Kalman filtering based on the model. The filtering result and the Allan variance analysis of FOG prove that the method effectively reduces the FOG random error, decreasing the angle random walk, zero-bias instability, rate random walk, angular rate ramp and quantification noise of FOG signals to less than one half of the corresponding values before the filtering of FOG random errors, which improves the accuracy of FOG.

GREEN FUNCTION APPROACH FOR THE ONE-DIMENSION FERRIMAGNETIC CHAIN WITH ALTERNATING SPINS 1 AND 1/2

2001 ◽  
Vol 15 (12) ◽  
pp. 1855-1865 ◽  
Author(s):  
GANG XIE ◽  
BIN CHEN ◽  
RUSHAN HAN
Keyword(s):  
Green Function ◽  
Physical Properties ◽  
Numerical Method ◽  
Spin Chain ◽  
One Dimension ◽  
Approximate Approach ◽  
Theoretical Approaches ◽  
Transcendental Equations ◽  
The One ◽  
Green Function Approach

We present Green Function's decoupling approximate approach for the ferrimagnetic spin chain with alternating spins 1 and 1/2, and a numerical method for solving two transcendental equations. And we compare some of our results with those from other theoretical approaches, such as the dependence of χT on T, where χ denotes susceptibility and T temperature. Moreover, we discuss some physical properties of our results.

Simulation of Random Differential Periodontitis Outcome Misclassification with Perfect Specificity

2021 ◽  
pp. 238008442110071
Author(s):  
T.S. Alshihayb ◽  
B. Heaton
Keyword(s):  
Periodontal Disease ◽  
Risk Ratio ◽  
Random Error ◽  
Association Studies ◽  
Quantitative Information ◽  
Random Errors ◽  
Case Definitions ◽  
Disease Etiology ◽  
Classification Errors ◽  
Differential Misclassification

Introduction: Misclassification of clinical periodontitis can occur by partial-mouth protocols, particularly when tooth-based case definitions are applied. In these cases, the true prevalence of periodontal disease is underestimated, but specificity is perfect. In association studies of periodontal disease etiology, misclassification by this mechanism is independent of exposure status (i.e., nondifferential). Despite nondifferential mechanisms, differential misclassification may be realized by virtue of random errors. Objectives: To gauge the amount of uncertainty around the expectation of differential periodontitis outcome misclassification due to random error only, we estimated the probability of differential outcome misclassification, its magnitude, and expected impacts via simulation methods using values from the periodontitis literature. Methods: We simulated data sets with a binary exposure and outcome that varied according to sample size (200, 1,000, 5,000, 10,000), exposure effect (risk ratio; 1.5, 2), exposure prevalence (0.1, 0.3), outcome incidence (0.1, 0.4), and outcome sensitivity (0.6, 0.8). Using a Bernoulli trial, we introduced misclassification by randomly sampling individuals with the outcome in each exposure group and repeated each scenario 10,000 times. Results: The probability of differential misclassification decreased as the simulation parameter values increased and occurred at least 37% of the time across the 10,000 repetitions. Across all scenarios, the risk ratio was biased, on average, toward the null when the sensitivity was higher among the unexposed and away from the null when it was higher among the exposed. The extent of bias for absolute sensitivity differences ≥0.04 ranged from 0.05 to 0.19 regardless of simulation parameters. However, similar trends were not observed for the odds ratio where the extent and direction of bias were dependent on the outcome incidence, sensitivity of classification, and effect size. Conclusions: The results of this simulation provide helpful quantitative information to guide interpretation of findings in which nondifferential outcome misclassification mechanisms are known to be operational with perfect specificity. Knowledge Transfer Statement: Measurement of periodontitis can suffer from classification errors, such as when partial-mouth protocols are applied. In this case, specificity is perfect and sensitivity is expected to be nondifferential, leading to an expectation for no bias when studying periodontitis etiologies. Despite expectation, differential misclassification could occur from sources of random error, the effects of which are unknown. Proper scrutiny of research findings can occur when the probability and impact of random classification errors are known.

Sign in / Sign up

Export Citation Format

Share Document