Distribution Of Random Errors Research Articles

Solution for heterogeneous data fusion based on autonomous classification

Variance component estimation (VCE) is an essential component of heterogeneous data fusion, however, VCE has problems with stability and reliability in random models. To progress data fusion research, this paper proposes a new solution that establishes a data fusion model based on the theory of Msplit estimation. To determine the classification number of heterogeneous data accurately, a median function was applied for autonomous classification using Msplit estimation, according to the basic characteristics of random error distribution, a method of autonomous classification is established for heterogeneous data. Especially, the fusion method presented in this paper does not rely on prior information of observation data and can effectively overcome the limitations of current methods for data fusion based on the theory of VCE. An example of coordinate affine transformation was used to verify that the model proposed in this paper could achieve effective fusion of heterogeneous data.

Angle Expansion Estimation and Correction Based on the Lindeberg–Feller Central Limit Theorem Under Multi-Pulse Integration

The radar monopulse angle measurement can obtain a target’s angle information within a single pulse, meaning that factors such as target motion and amplitude fluctuations, which vary over time, do not affect the angle measurement accuracy. However, in practical applications, when a target’s signal-to-noise ratio (SNR) is low, the single pulse signal is severely affected by noise, leading to a significant deterioration in angle measurement accuracy. Therefore, it is usually necessary to coherently integrate multiple pulses before estimating the angle. This paper constructs an angle expansion model for a multi-pulse angle measurement under coherent integration. The analysis reveals that even under noise-free conditions, after coherently integrating multiple pulses, the coupling of target amplitude fluctuations and motion state can still cause significant errors in the angle measurement. Subsequently, this paper conducts a detailed analysis of the impact of the amplitude fluctuations and target maneuvers on the random angle measurement error. It also derives approximate probability density functions of angle measurement errors under various fluctuation and motion scenarios based on the Lindeberg–Feller central limit theorem. In addition, based on the angle expansion model and the random error distribution, this paper proposes an angle correction algorithm based on multi-pulse integration and long-term estimation. Numerical experiments and radar data in the field verify the impact of target characteristics on the angle measurement under multi-pulse integration and the effectiveness of the angle correction algorithm.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

The first investigation of the dosimetric perturbations from the spot position errors in spot-scanning arc therapy (SPArc)

Objective. To quantitatively investigate the impact of spot position error (PE) on the dose distribution in (Spot-scanning arc therapy) SPArc plans compared to Intensity-Modulated Proton Therapy (IMPT). Approach. Twelve representative cases, including brain, lung, liver, and prostate cancers, were retrospectively selected. Spot PEs were simulated during dynamic SPArc treatment delivery. Two types of errors were generated, including random error and systematic error. Two different probability distributions of random errors were used (1) Gaussian distribution (PEran-GS) (2) uniform distribution (PEran-UN). In PEran-UN, four sub-scenarios were considered: 25%, 50%, 75%, and 100% spots were randomly selected in various directions on the scale of 0–1 mm or 0–2 mm of PE. Additionally, systematic error was simulated by shifting all the spot uniformly by 1 or 2 mm in various directions (PEsys). Gamma-index Passing Rate (GPR) is applied to assess the dosimetric perturbation quantitatively. Main results. For PEran-GS in the 1 mm scenario, both SPArc and IMPT are comparable with a GPR exceeding 99%. However, for PEran-GS in 2 mm scenario, SPArc could provide better GPR. As PEsys of 2 mm, SPArc plans have a much better GPR compared to IMPT plans: SPArc’s GPR is 99.59 ± 0.47%, 93.82 ± 4.07% and 64.58 ± 15.83% for 3 mm/3%, 2 mm/2% and 1 mm/1% criteria compared to IMPT with 97.49 ± 2.44%, 84.59 ± 4.99% and 42.02 ± 6.31%. Significance. Compared to IMPT, SPArc shows better dosimetric robustness in spot PEs. This study presents the first simulation results and the methodology that serves as a reference to guide future investigations into the accuracy and quality assurance of SPArc treatment delivery.

Research on Quantile Regression Method for Longitudinal Interval-Censored Data Based on Bayesian Double Penalty

The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China.

Влияние удовлетворенности условиями труда на здоровье работников

The study investigates the effect of satisfaction with working conditions on health of the Russian working population, disaggregated by gender and age groups. The author uses a copula-based recursive system of binary equations. It allows to account for the endogeneity of working conditions satisfaction and to consider different partial distributions of random errors and their dependence structure as separate tasks. The findings indicate that satisfaction with working conditions plays a protective role in maintaining employee health, with age differentiation in effect size, particularly among male individuals.

The a Priori Procedure (APP) for Estimating the Cohen’s Effect Size for Matched Pairs Under Skew Normal Settings

The a priori procedure (APP) provides minimum sample sizes to meet specifications for precision and confidence that, in turn, can enhance trust that the sample statistics to be obtained provide good estimates of corresponding population parameters. A recent advance by Chen et al.3 showed how to perform the APP with respect to Cohen’s [Formula: see text], which is the most popular effect size measure in the social sciences. However, a limitation is that Chen et al.3 assumed normal distributions that compose only a subset of the much larger family of skew normal distributions, which are used as distributions of random errors in many economical models such as stochastic frontier models that are popular and useful models to investigate production efficiency in microeconomics, see Hung.5 Therefore, it would be useful to generalize to skew normal distributions. We perform the mathematical derivations for the generalization and support them with simulations and worked examples. Finally, we provide a free and user-friendly computer program by which researchers can perform the APP to determine minimum sample sizes necessary to meet specifications for precision and confidence, with respect to Cohen’s [Formula: see text], for a matched sample under the large umbrella of skew normal distributions.

Estimating Treatment Effects of Disease‐modifying Drugs: Traditional Methods vs. Accelerated Failure Time Models and Progression Analysis

AbstractBackgroundProgression models for repeated measures (PMRM1) are a class of statistical models that enable estimation of slowing of progression of Alzheimer’s disease, expressed as percentage or time delay. Similarly, accelerated failure time (AFT) models can estimate relative expected time until progression when evaluating disease‐modifying therapies. We compared these methods to mixed‐effects models for repeated measures (MMRM) and Cox time‐to‐event analysis on simulated trial data, evaluating their power and the difference in interpretation when expressing outcomes as a measure of time.MethodPrimary outcomes were Clinical Dementia Rating (CDR) Sum of Boxes (MMRM and PMRM) and time to progression to dementia as assessed by CDR global (Cox regression and AFT models). Weibull and log‐logistic distributions were assumed for random error distribution in AFT models.Subject‐level placebo arm trajectories were jointly simulated based on estimated CDR mean trajectories and joint temporal correlation structure of 538 amyloid‐positive MCI patients meeting typical disease‐modifying trial inclusion criteria from the ADNI study. Active arm trajectories were simulated to show an average 20% slowing of disease progression vs placebo at each visit. A thousand simulations were conducted across scenarios, varying number of subjects per arm (200‐700) and clinical trial duration (18‐36 months).ResultPower of PMRM was shown to be consistently greater than that of MMRM (Table 1). The AFT and Cox models’ power rarely exceeded 40%.PMRM accurately estimated the underlying 20% slowed progression. With greater sample sizes and at least 2 years of follow‐up, the AFT models indicated a slowing of progression, but the median estimated slowing was 5%. The MMRM and Cox model found median estimated reduction in decline of 25% and median estimated hazard ratios of 0.88‐0.91, respectively.ConclusionsPMRM and AFT models estimate slowing of progression. Compared to the MMRM and Cox model, these time‐based models better capture the effect of disease‐modifying therapies and facilitate translation of results to patients and their care partners. Among all methods studied, the PMRM offered the best combination of interpretability and power.

Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors.

In this work, we present a methodology for predicting the optical performance impacts of random and structured MSF surface errors using pupil-difference probability distribution (PDPD) moments. In addition, we show that, for random mid-spatial frequency (MSF) surface errors, performance estimates from the PDPD moments converge to performance estimates that assume random statistics. Finally, we apply these methods to several MSF surface errors with different distributions and compare estimated optical performance values to predictions based on earlier methods assuming random error distributions.

Test-retest reliability of joint position sense in the elbow among healthy adults

BackgroundProprioception of the elbow is necessary for daily activities. Proprioception can be impaired with injury or pathology, and rehabilitation efforts seek to improve proprioception for improved upper extremity functioning. In clinical practice, joint position sense (JPS) testing is often utilized to assess conscious proprioception; however, varying methods exist with little evidence of psychometric properties, especially for the elbow. PurposeThe primary aim of this study was to create a standardized elbow JPS test protocol using goniometry measurement to determine the most reliable testing position. The secondary aim was to determine if the elbow JPS test had acceptable test-retest reliability in healthy adults. Study DesignThis was a cross-sectional study using a convenience sample of healthy adults. MethodsThree elbow positions (45°, 60°, and 75° of elbow flexion) were measured twice on the same day by a single rater using a universal goniometer. We calculated the absolute error in degrees between each position and reposition and the intraclass correlation coefficient (3,1) for relative reliability. We also calculated the standard error of the measurement and visually inspected Bland-Altman plots for absolute reliability. ResultsSixty-eight healthy adults (mean age 27.9 years, standard deviation 8.59) were assessed. The mean absolute error for all positions for test and retest was 5.7°. The intraclass correlation coefficients were moderate to good (0.57-0.75), and the standard error of the measurement was 2° (rounded) for all positions. The limits of agreement were moderately narrow, and the Bland-Altman plots showed a random distribution of errors for each position, indicating clinically acceptable measurement error. ConclusionsThe joint position reproduction test for JPS using goniometry demonstrated moderate to good test-retest reliability and acceptable measurement error in healthy adults. The elbow joint angle of 60° flexion was the most reliable for JPS testing, providing insight for JPS assessment in clinical practice.

Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability

We present weight distribution of low-density periodic random errors in the space of all q-ary n-tuples along with the average Hamming weight of the error set. We also provide necessary and sufficient conditions for the existence of linear codes correcting such error pattern. Examples of such codes are given. Finally, probability of decoding error of such codes over a binary symmetric channel is derived.

Interfractional diaphragm and abdominal organ motion in 189 children during radiotherapy: a multicenter study

<h3>Objectives</h3> For adequate radiotherapy in thoracic-abdominal tumors, organ motion needs to be considered in treatment planning. Although margin definitions for children have been reported, comprehensive analyses on applicable margins for treatment planning remain scarce. We aimed to quantify interfractional organ motion in a large multicenter patient cohort, and to investigate correlations with age and with general anesthesia (GA). <h3>Methods</h3> Interfractional motion of both diaphragm domes, spleen, liver and kidneys relative to bony anatomy was quantified in 189 children (mean age 8.2; range 0.4–17.9 years), using 271 reference CT and 2052 cone beam CT scans. We calculated the distributions of systematic and random errors (standard deviations Σ and σ, respectively) in cranio-caudal (CC), left-right and anterior-posterior directions. Besides correlations between organ motion and age we investigated motion differences in a subcohort of patients <7 years treated with and without GA. <h3>Results</h3> For all organs (all directions) interfractional group mean motion was not significantly different compared to the CT (Bonferroni's adjusted p=0.008). Calculated Σ and σ were larger for diaphragm domes, liver and spleen compared to values for the kidneys (Table). We found no correlations between organ motion and age (r<0.1; p>0.05). Motion of both diaphragm domes, liver and spleen in CC direction for patients (<7 years) treated with GA was significantly smaller compared to those treated without GA (p<0.008), resulting in smaller Σ and σ for both diaphragm domes and three organs (Table). <h3>Conclusion</h3> Motion quantification in a large cohort resulted in good estimations of interfractional Σ and σ values. There were no correlations between motion and age, but the use of GA in young patients showed significantly less motion, with subsequently small differences in Σ and σ values between groups.

Determination of constant and variable thermal diffusivity of cashew pulp during heating: Experimentation, optimizations and simulations

Cashew nut is used by the industry in the production of roasted kernels, whose flavor is appreciated in various parts of the world. However, the production of 1 ton of roasted kernels generates up to 15 tons of cashew apple, which is a highly perishable by-product. To increase its shelf life, cashew apple can be transformed into pulp, which is then pasteurized. Designing efficient pasteurizers requires knowledge of the thermal diffusivity of this product, in the heating step. Thus, an experiment was carried out with heating of this pulp placed in a metallic cylinder (from 25.6 °C to 63.1 °C), in a water bath (at 63.1 °C), with a thermocouple fixed at the central point of the product. Thermal diffusivity was determined through the inverse method, using analytical and numerical solutions of the diffusion equation. The use of a variable thermal diffusivity, given as a function of the local temperature, expressed by α(T) = a1cosh(a2T2), produced excellent fit of the simulation to the experimental data, with random distribution of errors, and with χ2 = 0.1626 and R2 = 0.999984.

Stepwise algorithm for estimating intraparticle diffusivity by zero-length-column desorption experiments

There are two problems with intraparticle diffusivity estimation by Zero-length-column (ZLC) desorption experiment: 1) no viable algorithm for producing reliable accuracy estimation, and 2) difficulty in fitting short- and long-term ZLC data to the series solution. To tackle these problems, we propose replacing direct curve-fitting with an algebraic-equation solving followed by a single-parameter curve fitting. This stepwise algorithm uncouples parameters' estimation and facilitates the series-solution fitting. Moreover, the stepwise method can yield from one experimental run multiple parameter estimates, a set of estimates containing the information of random error distribution. This set of estimates provides a direct way of deriving statistics quantifying the parameter-estimation uncertainty, such as variance, standard deviation, confidence interval, etc. The new method was validated by using two independently reported ZLC data sets, and its idea is general and applies to other inverse problems of heat and mass transfer.

Evaluating the Accuracy of the Azure Kinect and Kinect v2.

The Azure Kinect represents the latest generation of Microsoft Kinect depth cameras. Of interest in this article is the depth and spatial accuracy of the Azure Kinect and how it compares to its predecessor, the Kinect v2. In one experiment, the two sensors are used to capture a planar whiteboard at 15 locations in a grid pattern with laser scanner data serving as ground truth. A set of histograms reveals the temporal-based random depth error inherent in each Kinect. Additionally, a two-dimensional cone of accuracy illustrates the systematic spatial error. At distances greater than 2.5 m, we find the Azure Kinect to have improved accuracy in both spatial and temporal domains as compared to the Kinect v2, while for distances less than 2.5 m, the spatial and temporal accuracies were found to be comparable. In another experiment, we compare the distribution of random depth error between each Kinect sensor by capturing a flat wall across the field of view in horizontal and vertical directions. We find the Azure Kinect to have improved temporal accuracy over the Kinect v2 in the range of 2.5 to 3.5 m for measurements close to the optical axis. The results indicate that the Azure Kinect is a suitable substitute for Kinect v2 in 3D scanning applications.

Exploration of new analytical correlations as an alternative to the Kramers-Kronig transforms for the assessment of impedance spectroscopy data

• Alternative method to detect errors in EIS spectra. • Overcome of some practical issues for assessment of simple spectra. • Elucidation of analytical correlations between magnitude and phase. New analytical correlations between impedance magnitude and phase are developed and presented. These correlations are used for the assessment of impedance spectroscopy data. As correlations are obtained, they can be calculated point to point at each frequency of the spectra with no need to establish explicit premises related to stability, linearity or finite limits for their derivation. Their use is simpler than that based on the direct evaluation of the Kramers-Kroning transforms or alternative methods. An example of their derivation from basic equations involving complex numbers is described. They were obtained by looking for an explanation of the empirical fact that the slope of the Bode-Magnitude diagram vs frequency resembles the shape of the corresponding Bode-Phase diagram. Unlike the Kramers-Kronig transform, these new correlations can also be directly applied to test spectra with highly predominant capacitive or inductive responses or even incomplete loops. Their analytical expressions are exact for simple ideal elements and circuits, including the Warburg diffusion element. These correlations were tested with simulated spectra altered with known random error distributions, and they were able to detect the random distribution and the error level for simple spectra when the errors were > 0.5%. For more sophisticated spectra, the minimum error that can be detected without interference of the deviations due to the proper algorithm are around 2.5%. No exact correlation was found for a constant phase element (CPE), but a close empirical approximation was obtained for a single CPE. It is necessary to improve this approximation when a CPE is combined with some other elements because of detected deviations. In addition, it was found that in a first approach the algorithm does not detect non-linear behavior on a simple experimental circuit, but the test gave insights of how to detect it. On the contrary, it is well suited for detection of system stability issues. Examples of their application to actual experimental spectra, high capacitive or with several loops, are presented and the limitations discussed. More work and exhaustive tests are necessary to improve the method and stablish its real limitations, but its use for assessment of simple spectra at certain error level can already be done. Given that the derivation of the new correlations is only based on its complex number nature, this study concludes that the magnitude and phase of any complex number or 2D vector are not independent, and it is expected that similar correlations can be applied to any frequency-dependent complex variable, vector or transfer function, such as those used in optics or rheology.

Investigating the effects of random data errors on the waveform-based moment tensor inversion

SUMMARY The linear Gauss–Markov model for waveform-based moment tensor inversion often relies on the overdetermined least-squares method. It needs a proper stochastic model of the observables for accurate and precise estimates of the unknown parameters. Furthermore, estimating the level and distribution of random errors in the observed waveforms is challenging due to assessing the minimum-variance unbiased estimator (MVUE). Hence, according to the considerable effects of random data errors in assessing the uncertainty of the moment tensor components, this paper aims to describe an MVUE of the data covariance matrix and its application on uncertainty quantification of the moment tensor. The used mathematical prescription allows us to use the covariance matrix for the three-component noise records at every station and all possible cross-correlations among the recorded noise wavefield. To illustrate the proposed method’s performance, we conducted tests with synthetic data using configuration of the 2018 Mw 6.8 Zakynthos (Ionian Sea, Greece) earthquake. Both uncorrelated and correlated random noise traces were added to the synthetic waveform data in amounts between 5 and 20 per cent of the maximum amplitude. In order to test the efficiency of the method, we considered three different structures of covariance matrix: (i) diagonal matrix (contains a variance of individual measurements at seismic stations), (ii) block-diagonal matrix (considering cross-covariance among three components at each station), and (iii) full covariance matrix. Test results are presented by comparison of the moment tensor inversion outcomes with known noise levels of generated synthetic data and with synthetic focal mechanisms, the ability of the estimated full covariance matrix in illustrating the minimum variance of parameters (namely, minimum posterior uncertainties), unbiased of the parameters, and values of the cross-correlations between the components of each station and also among stations. Finally, we applied the method to the real waveforms of the Zakynthos earthquake having inferred focal mechanism of strike/dip/rake angles 13/40/171 (deg) with 33 per cent double couple (DC) and −61 per cent compensated linear vector dipole component (CLVD). The focal mechanism solution has strike/dip/rake angles 19/34/177 (deg) with 69 per cent DC and −23 per cent CLVD when using our estimated full covariance matrix.

Parameters' Confidence Intervals Evaluation for Heterogeneous Strain Field Specimen Designs by Using Digital Image Correlation

This paper aims to compare different heterogeneous test designs from the perspective of the confidence interval quantification of inversely identified parameters, where the influence of a DIC optical system systematic and random error are taken into account. Because the errors in optical measurement can arise from many reasons and sources, our methodology relies on the system's errors determined from initial sets of pictures acquired at the load-free state for hundreds of specimens (over 850 tests over the past three years). In this way, a prior probability distribution of systematic and random error, arisen from the system initial settings and testing procedures are determined. Further, by conducting an inverse identification procedure of linear orthotropic elastic material parameters, the influence of the error distributions is studied for different types of heterogeneous specimens. The presented methodology determines the DIC bias and random error propagation through the inverse identification procedure to individual parameters. For each specimen design, confidence intervals of identified material parameters were determined. The results show the appropriateness of a specimen design for the identification of particular material parameters.

Parametric Versus Semi and Nonparametric Regression Models

There are three common types of regression models: parametric, semiparametric and nonparametric regression. The model should be used to fit the real data depends on how much information is available about the form of the relationship between the response variable and explanatory variables, and the random error distribution that is assumed. Researchers need to be familiar with each modeling approach requirements. In this paper, differences between these models, common estimation methods, robust estimation, and applications are introduced. For parametric models, there are many known methods of estimation, such as least squares and maximum likelihood methods which are extensively studied but they require strong assumptions. On the other hand, nonparametric regression models are free of assumptions regarding the form of the response-explanatory variables relationships but estimation methods, such as kernel and spline smoothing are computationally expensive and smoothing parameters need to be obtained. For kernel smoothing there two common estimators: local constant and local linear smoothing methods. In terms of bias, especially at the boundaries of the data range, local linear is better than local constant estimator.&amp;nbsp; Robust estimation methods for linear models are well studied, however the robust estimation methods in nonparametric regression methods are limited. A robust estimation method for the semiparametric and nonparametric regression models is introduced.

Statistical point cloud model to investigate measurement uncertainty in coordinate metrology

In this work an approach to investigate measurement uncertainty in coordinate metrology is presented, based on fitting Gaussian random fields to high-density point clouds produced by measurement repeats. The fitted field delivers a depiction of the spatial distribution of random measurement error over a part geometry, and can incorporate local bias information through further measurement or with the use of an external model to obtain a complete, spatial uncertainty map. The statistical model also allows the application of Monte Carlo simulation to investigate how error propagates through the data processing pipeline ultimately affecting the determination of features of size and the verification of conformance to specifications. The proposed approach is validated through application to simulated test cases involving known measurement error, and then applied to a real part, measured with optical and contact technologies. The results indicate the usefulness of the approach to estimate measurement uncertainty and to investigate performance and behaviour of measurement solutions applied to the inspection and verification of industrial parts. The approach paves the way for the implementation of automated measurement systems capable of self-assessment of measurement performance.