Statistical Error Research Articles

Fast and accurate peak skin dose estimation method for interventional fluoroscopy patients.

In fluoroscopy, particularly fluoroscopically guided interventions (FGIs), accurate estimation of peak skin dose (PSD) is crucial for identifying potential radiation-induced skin injuries. Most current methodologies for PSD calculation methods rely on analytical methods, which may introduce uncertainty due to their limited consideration of the complexities of x-ray beam conditions, patient geometry, and positioning. Methods based on full Monte Carlo (MC) simulations can enhance accuracy, but their practical application is limited due to the intensive requirement of computational resources and time. We aimed to develop a novel method that combines MC simulation with a noise reduction technique to calculate PSD, as well as skin dose distributions, more efficiently and accurately. The goal was to overcome the limitations of current methods, providing a more practical solution for clinical and academic use. Our method to calculate the PSD and skin dose distributions consists of two steps of rough MC simulation and iterative noise reduction. The performance of the methodology was demonstrated for six fluoroscopy scenarios, with results compared against those from full MC simulation with high particle history, which is considered a gold standard for radiation dosimetry relative to conventional analytical methods. Our method was demonstrated for various fluoroscopy scenarios, and the result showed that the iterative noise reduction procedure successfully estimates PSD and skin dose distribution for rough MC simulations with a maximum dose statistical error of up to 20%. For successful dose estimations, PSD discrepancies from the values obtained by full MC simulation were within 3%, and voxel-wise dose differences in skin dose distributions were less than 10% of the average skin dose. The computation time of our method was on the order of a few seconds on a personal computer, which is estimated to be at least 104 times faster than full MC simulation when using the same computing resources. Our method rapidly and accurately calculates PSD and skin dose distribution, making it a useful tool for research and clinical applications. The planned integration of our method into the National Cancer Institute Dosimetry System for Radiography and Fluoroscopy (NCIRF) will enhance accessibility. Additionally, future upgrades of NCIRF will include a comprehensive phantom library and pregnant phantoms that will enable our method to account for patient-specific body shapes, further improving the accuracy and personalization in dose assessments.

Radar–Rain Gauge Merging for High-Spatiotemporal-Resolution Rainfall Estimation Using Radial Basis Function Interpolation

This study introduces methods for generating fused precipitation data by applying radial basis function (RBF) interpolation, which integrates radar reflectivity-based data with ground-based precipitation gauge measurements. Rain gauges provide direct point rainfall measurements near the ground, while radars capture the spatial variability of precipitation. However, radar-based estimates, particularly for extreme rainfall events, often lack accuracy due to their indirect derivation from radar reflectivity. The study aims to produce high-resolution gridded ground precipitation data by merging radar rainfall estimates with the precise rain gauge measurements. Rain gauge data were sourced from automated synoptic observing systems (ASOSs) and automatic weather systems (AWSs), while radar data, based on hybrid surface rainfall (HSR) composites, were all provided by the Korea Meteorological Administration (KMA). Although RBF interpolation is a well-established technique, its application to the merging of radar and rain gauge data is unprecedented. To validate the accuracy of the proposed method, it was compared with traditional approaches, including the mean field bias (MFB) adjustment method, and kriging-based methods such as regression kriging (RK) and kriging with external drift (KED). Leave-one-out cross-validation (LOOCV) was performed to assess errors by analyzing overall error statistics, spatial errors, and errors in rainfall intensity data. The results showed that the RBF-based method outperformed the others in terms of accuracy.

Error fields: personalized robotic movement training that augments one’s more likely mistakes

Control of movement is learned and uses error feedback during practice to predict actions for the next movement. We previously showed that augmenting error can enhance learning, but while such findings are encouraging, the methods need to be refined to accommodate a person’s individual reactions to error. The current study evaluates error fields (EF) method, where the interactive robot tempers its augmentation when the error is less likely. 22 healthy participants were asked to learn moving with a visual transformation, and we enhanced the training with error fields. We found that training with error fields led to greatest reduction in error. EF training reduced error 264% more than controls who practiced without error fields, but subjects learned more slowly than our previous error magnification technique. These robotic training enhancements should be further explored in combination to optimally leverage error statistics to teach people how to move better. This study reports results from a clinical trial registered on ClinicalTrials.gov with ID: NCT02720341.

A Model and Data Dual-Driven Framework for Lithium-Ion Battery Cycle Life Prediction Integrating Uncertainty Model

Abstract To address the shortcomings of single model-based or data-driven methods in battery life prediction, this paper proposes a model and data dual-driven framework for lithium-ion battery (LIB) cycle life prediction integrating uncertainty model. First, a cloud model is used to quantify the uncertainty inherent in the empirical model and construct a capacity degradation uncertainty model. Next, health features highly correlated with capacity are extracted from historical data to train a convolutional neural network, forming an online estimation model that guides subsequent parameter correction. Then, based on the prediction discrepancy between the two models, the error-feedback gate recurrent unit with improved attention model is developed for the online dynamic correction of empirical model parameters, realizing a closed-loop prediction framework. Finally, a rolling correction strategy based on statistical error is proposed to dynamically adjust the cloud model parameters, with the corrections fed back to the capacity degradation uncertainty model to further refine prediction uncertainty and accuracy. Experimental results indicate that the proposed method achieves high accuracy across various battery datasets, with relative error remaining below 2%, and provides uncertainty-quantified remaining useful life prediction, which effectively supports the online health monitoring and maintenance strategy formulation of LIBs in diverse scenarios.

Insights into Dermal Permeation of Skin Oil Oxidation Products from Enhanced Sampling Molecular Dynamics Simulation.

The oxidation of human sebum, a lipid mixture covering our skin, generates a range of volatile and semivolatile carbonyl compounds that contribute largely to indoor air pollution in crowded environments. Kinetic models have been developed to gain a deeper understanding of this complex multiphase chemistry, but they rely partially on rough estimates of kinetic and thermodynamic parameters, especially those describing skin permeation. Here, we employ atomistic molecular dynamics simulations to study the translocation of selected skin oil oxidation products through a model stratum corneum membrane. We find these simulations to be nontrivial, requiring extensive sampling with up to microsecond simulation times, in spite of employing enhanced sampling techniques. We identify the high degree of order and stochastic, long-lived temporal asymmetries in the membrane structure as the leading causes for the slow convergence of the free energy computations. We demonstrate that statistical errors due to insufficient sampling are substantial and propagate to membrane permeabilities. These errors are independent of the enhanced sampling technique employed and very likely independent of the precise membrane model.

Quantitative error analysis of polarimetric phased-array radar weather measurements to reveal radar performance and configuration potential

Abstract. The initial weather measurements from two polarimetric phased-array radars (PPARs) with cylindrical and planar configurations, both developed by the Advanced Radar Research Center (ARRC) at the University of Oklahoma (OU), were compared with those from the dish antenna systems, the operational KTLX Weather Surveillance Radar 1988 Doppler (WSR-88D) located in Oklahoma City, Oklahoma (∼ 23 km northeast of OU). Both the cylindrical PPAR (CPPAR) and the planar PPAR (PPPAR) Horus are S-band two-dimensional (2D) electronic scan PPARs. This comparison investigates the error statistics of the polarimetric measurements in one-dimensional (1D) electronic scans from each radar during two convective rain events. The first event occurred on 30 August 2019, when the CPPAR performed a 3.3° elevation plan-position indicator (PPI) scan at 25 azimuth angles. The second event took place on 4 October 2023, when Horus conducted range–height indicator (RHI) scans at 64 elevations. For both events, KTLX provided volumetric polarimetric radar data and served as the reference. To ensure temporal and spatial alignment between the radars, reconstructed RHI scans and PPI sectors from KTLX were matched to the corresponding Horus rays and CPPAR domain, respectively. The standard deviations and mean biases of the PPAR weather measurements were calculated and analyzed. The standard deviations of the two PPARs were similar and met the Radar Functional Requirements (RFR) set by the National Oceanic and Atmospheric Administration National Weather Service. However, as noted in previous studies, the standard deviation and biases of polarimetric variables from Horus exhibited varying error characteristics depending on the electronic steering angle from broadside. The present results suggest that PPPARs may have difficulties in producing high-quality polarimetric data at large steering angles, and further investigation on CPPARs is required to find the optimal design for future weather applications.

Clustering-Based Hybrid Model for Predicting Symptoms for Colorectal Cancer: A Fuzzy Machine Learning Approach

Colorectal cancer (CRC) is a form of cancer that originates in the colon (large intestine) or rectum, which are components of the digestive system. It generally begins as small, benign growths known as polyps that can form on the inner lining of the colon or rectum. In Malaysia, colorectal cancer ranks among the most prevalent cancers, especially within the Chinese and Malay communities. A study released by the Malaysian National Cancer Registry indicates that colorectal cancer is the second most common cancer type following breast cancer, impacting both genders. The occurrence of colorectal cancer in Malaysia has been consistently increasing, with approximately 15–20% of cancer cases in the nation being colorectal cancer. This type of cancer arises when cells in the body start to multiply excessively, leading to various symptoms. In this research, a novel hybrid fuzzy linear regression with symmetric parameter clustering combined with a support vector machine (FLRWSPCSVM) model is employed to predict the high-risk symptoms associated with the onset of colorectal cancer in Malaysia. The study analyzed secondary data from 180 patients diagnosed with colorectal cancer and treated in a general hospital in Kuala Lumpur, considering twenty-five independent variables with various combinations of variable types. Furthermore, the model included parameters, errors, and explanations, along with two statistical measurement errors. The findings revealed that FLRWSPCSVM identified ovarian symptoms and a history of cancer symptoms as high-risk indicators for the development of colorectal cancer, with the lowest mean square error (MSE) recorded at 100.605 and a root mean square error (RMSE) of 10.030.

Common statistical errors in systematic reviews: A tutorial

AbstractThe aim of this article is to present the most common statistical errors in meta‐analyses included in systematic reviews; these are confusing standard deviation and standard error, using heterogeneity estimators for choosing between a common‐effect and random‐effects model, improper handling of multiarm trials, and unnecessary and misinterpreted subgroup analyses. We introduce some useful terminology and explain what authors can do to avoid these errors and how peer reviewers can spot them. We have also developed a micro‐learning module to provide practical hands‐on tutorial.

Tropospheric ozone sensing with a differential absorption lidar based on a single CO2 Raman cell

Abstract. This study presents the development and performance evaluation of an ozone differential absorption lidar system. The system could effectively obtain vertical profiles of lower-tropospheric ozone in an altitude range of 0.3 to 4 km with high spatiotemporal resolutions. The system emits three laser beams at wavelengths of 276, 287 and 299 nm by using the stimulated Raman effect of carbon dioxide (CO2). A 250 mm telescope and a grating spectrometer are used to collect and separate the backscattering signals at the three wavelengths. Considering the influences of aerosol interference and statistical error, a wavelength pair of 276–287 nm is used for the altitude below 600 m and a wavelength pair of 287–299 nm is used for the altitude above 600 m to invert ozone concentration. We also evaluated the errors caused by the uncertainty of the wavelength index. The developed ozone lidar was deployed in a field campaign that was conducted to measure the vertical profiles of ozone using a tethered balloon platform. The lidar observations agree very well with those of the tethered balloon platform.

Performance Assessment of a Coupled Circulation–Wave Modelling System for the Northwest Atlantic

We present a modified version of a coupled circulation–wave modelling system for the northwest Atlantic (CWMS-NWA) by including additional physics associated with wave–current interactions. The latest modifications include a parameterization of Langmuir turbulence and surface flux of turbulent kinetic energy from wave breaking in vertical mixing. The performance of the modified version of CWMS-NWA during Hurricane Arthur in 2014 is assessed using in situ measurements and satellite data. Several error statistics are used to evaluate the model performance, including correlation (R), root mean square error (RMSE), normalized model variance of model errors (γ2) and relative bias (RB). It is found that the simulated surface waves (R ≈ 94.0%, RMSE ≈ 27.5 cm, γ2≈ 0.16) and surface elevations (R ≈ 97.3%, RMSE ≈ 24.0 cm, γ2≈ 0.07) are in a good agreement with observations. The large-scale circulation, hydrography and associated storm-induced changes in the upper ocean during Arthur are reproduced satisfactorily by the modified version of CWMS-NWA. Relative to satellite observations of the daily averaged sea surface temperature (SST), the model reproduces large-scale features as demonstrated by the error metrics: R ≈ 97.8%, RMSE ≈ 1.6 ∘C and RB ≈ 8.6 ×10−3∘C.

On the pursuit of reproducibility: the importance of large sample sizes in psychoimmunology

Peripheral inflammatory markers (PIMs), such as C-reactive protein (CRP) or white blood cell count (WBC), have been associated with depression severity in meta-analyses and large cohort studies. However, in typically-sized psychoimmunology studies (N < 200) that explore associations between PIMs and neurobiological/psychosocial constructs related to depression and studies that examine less-studied PIMs (e.g., interferon gamma), significant concerns about reproducibility of results exist. For the well-characterized association between PIMs (CRP/WBC) and depression severity, we examined statistical errors as a function of sample size in a large community cohort (n = 24,550). We further assessed how statistical errors varied as related to analytic decisions (e.g., number of covariates) and characteristics related to study design (e.g., relationships within subgroups of patients). Only large samples (e.g., n = 1000 to n = 10,000) were sufficiently powered to detect PIM-depression associations and minimized overestimation of effect sizes (e.g., effect size inflation), and greater sample sizes were required as more covariates were included in analytic models. Moderately sized samples (n > 500) generally ensured the correct directionality of effect sizes (e.g., low rates of sign reversal). Sample sizes required for 80% power also varied widely depending on study design characteristics (e.g., N = 350 to N = 10,000+). Typically-sized psychoimmunology studies examining PIM-depression associations (N < 200) are likely underpowered and at high risk of overestimation of effect sizes. Study design characteristics also notably influence power and statistical error rates. Use of large sample sizes (e.g., N > 7000) and consideration of analytic decisions (e.g., number/choice of covariates) will maximize reproducibility of psychoimmunology studies related to depression to enhance development of treatments for depression or to help understand pathophysiological mechanisms of depression.

Determination of Equilibrium Loading by Empirical Models for the Modeling of Breakthrough Curves in a Fixed-Bed Column: From Experience to Practice

Empirical models have been found to be inadequate in both accounting for breakthrough behaviors and reflecting the performance of fixed-bed systems, primarily due to their lack of a robust theoretical foundation. This limitation severely restricts their practical application. To address this difficulty, the adjustable parameters of six empirical models were first determined using the Levenberg–Marquardt iteration algorithm. The fitting quality of these models was subsequently evaluated by several error statistics, including the reduced chi-square (χ2), adjusted coefficient of determination (Adj. R2), residual sum of squares (RSS) and root of mean squared error (RMSE). In addition, the Akaike information criterion (AIC) and Bayesian information criterion (BIC) were employed to further compare these empirical models with the different parameters. The equilibrium loading, breakthrough capacity and saturation capacity were then solved by the int command of MATLAB 2023b software. Meanwhile, the breakthrough time and saturation time were determined by its fzero command. Regardless of whether empirical or mechanistic models were used, the model with the asymmetric S-shaped curve could well describe the measured breakthrough curves. Based on the parallel sigmoidal model, the predicted equilibrium loadings were 101.11, 116.69 and 129.50 mg g−1, respectively, at adsorbent masses of 0.1, 0.3 and 0.5 g. This study aimed to conveniently obtain the critical process parameters through MATLAB software using empirical breakthrough models, thereby providing reliable information for the design and optimization of fixed-bed adsorbers.

DNA Triplet Energies by Free Energy Perturbation Theory.

Determining the energetics of triplet electronic states of nucleobases in the biological macromolecular environment of nucleic acids is essential for an accurate description of the mechanism of photosensitization and the design of drugs for cancer treatment. In this work, we aim at developing a methodological approach to obtain accurate free energies of triplets in DNA beyond the state of the art, able to reproduce the decrease of triplet energies measured experimentally for T in DNA (270 kJ/mol) vs in the isolated nucleotide in aqueous solution (310 kJ/mol). For such purposes, we adapt the free energy perturbation method to compute the free energy related to the transformation of a pure singlet state into a pure triplet state via "alchemical" intermediates with mixed singlet-triplet nature. By this means, standard deviation errors are only a few kJ/mol, contrary to the large errors of tenths of kJ/mol obtained by averaging the singlet and triplet energies derived from molecular dynamics simulations. The reduced statistical errors obtained by the free energy perturbation approach allow us to rationalize with confidence the triplet stabilization observed experimentally when comparing the thymine nucleotide and thymine in DNA. Spin polarization rather than excimer interactions between the π-stacked nucleobases originates the lower values of the triplet energies in DNA. The developed approach implemented in QM3 shall be useful for determining free energies of triplets and other states like ionic or charge separation states in any other macromolecular system with impact in biomedicine and materials science.

Heart Rate Variability Estimation Based on RFID Tag-Pair in Dynamic Environments

With the rapid development of smart health care, accurate heart rate variability (HRV) estimation for the early detection of diseases has become a hot research topic. Advanced work uses the wireless signal to estimate the heartbeat in a contact-free way, which usually cannot separate multiple users or work in a dynamic environment. In this article, we propose a lightweight heartbeat-sensing method based on RFID tag pairs, which focuses on HRV extraction in a more general sensing scenario. Based on the tag-pair design, we build a novel heartbeat and respiration model to describe the signal relationship between the two tags from the time and space domains. Based on the model, we propose a Calibrated Temporal-Spatial IQ-Shaping-based signal cancellation algorithm to cancel the respiration and extract the heartbeat. To remove the interference in dynamic measurement, we build an IQ-based signal model via a Principal Component Analysis-based interference estimation. To reduce the statistical error in HRV extraction, we further design a neural network to predict the HRV index. We have implemented a system prototype in a real environment with COTS RFID devices. Extensive experiments show that our system can achieve a median RMSSD error of 7.51 ms, which satisfies the medical demand in HRV measurement.

Lattice study of J/ψ→γηc using a method without momentum extrapolation

We present a model-independent method to calculate the radiative transition without the momentum extrapolation for the off shell transition factors. The on shell transition factor is directly obtained from the lattice hadronic function. We apply the method to calculate the charmonium radiative transition J/ψ→γηc. After a continuous extrapolation under three lattice spacings, we obtain the on shell transition factor as V(0)=1.90(4), where the error is the statistical error that already takes into account the a2 error in the continuous extrapolation. Finally, we determine the branching fraction of J/ψ→γηc as Br(J/ψ→γηc)=2.49(11)lat(5)exp%, where the second error comes from the uncertainty of J/ψ total decay width 92.6(1.7) keV. Published by the American Physical Society 2025

Updating pile bearing capacity estimation using multiple piling data and spatial correlation

ABSTRACT This paper proposes a method to comprehensively capture the variability of pile bearing capacity from the piling data within a site by Bayesian Gaussian process regression. The approach, based on the assumption that multiple piles are installed under controlled piling conditions, involves steps from obtaining piling data to calculating a credible interval on pile bearing capacity, considering spatial variability, piling variation and estimation error. To validate the proposed method, a field test was conducted with rotary cutting press-in piles. Three different input data and estimation methods were used, and their estimates were compared with rapid load test measurements. The proposed method successfully provided credible intervals that appropriately contained the measured values, and the estimated variances were generally in good agreement. The residuals of the estimation error fit the log-normal distribution well. The validity of the proposed method was confirmed for all three piling data inputs, demonstrating its versatility. Furthermore, the proposed method reduces the statistical error when identifying bias from comparisons with load tests. It would also increase the value of piling data, which has traditionally been difficult to use for small projects due to the requirement of additional load tests to identify inter-site errors in the piling data.

A comparative study of interpolation methods for the development of ore distribution maps

Mining projects require precise knowledge about tonnage and quality of ore reserves for planning and decision-making. This is hard to establish as exploration operations, which are costly, time-consuming and require an accurate description of the deposit. Geologists use deterministic and geostatistical methods as interpolation tools to generate a continuous (or prediction) ore distribution map from known sampled data. A comparative study between four different geostatistical interpolation techniques: Ordinary Kriging (OK), Simple Kriging (SK), Universal Kriging (UK) and Empirical Bayesian Kriging (EBK); and four deterministic techniques: Inverse Distance Weighting (IDW), Global Polynomial Interpolation (GPI), Radial Basis Function (RBF), and Local Polynomial Interpolation (LPI) were applied. The 95% confidence level was measured and the effectiveness of each interpolation method was assessed through cross-validation for the construction of the corresponding maps displaying the distribution of ore on the surface with the use of GIS. The output methods are ranked to perform a comprehensive analysis using the error statistics methods: Mean Error (ME), Root Mean Square Error (RMSE), Mean Standardized Error (MSE) and Root Mean Square Standardized Error (RMSSE). The results show that GPI, EBK and Kriging methods perform the best results while IDW has good statistical analysis factors but it came in the tail of the rank. Therefore, there is no appropriate interpolation method accurate for all cases, each method must be statistically evaluated before each application and essentially based on real data.

Comparison of Measurement Protocols for Internal Channels of Transparent Microfluidic Devices

The microfluidic industry faces a significant challenge due to the lack of sensitive and standardized methods. One critical need is the measurement of internal channel dimensions in fully assembled chips. This study presents and compares several protocols for measuring these dimensions, including optical profilometry, optical microscopy, and tiled digital imagery. Standardized chips made from two materials commonly used in microfluidics (borosilicate glass and Cyclic Olefin Copolymer) were evaluated using each protocol. A consistency analysis using normalized error statistics identified optical profilometry as the most reliable method, offering the lowest uncertainty and the highest consistency with nominal geometry values. However, all protocols encountered difficulties with vertical depth measurements of internal structures. Future research should focus on addressing these limitations, including investigating the influence of multiple refractive surfaces on optical profilometry and exploring confocal microscopy. In conclusion, this work provides a comprehensive comparison of measurement protocols for internal microfluidic structures and offers a practical solution for applications in the microfluidic industry, while also identifying important directions for future research.

Spatiotemporal Interpolation of Actual Evapotranspiration Across Turkey Using the Australian National University Spline Model: Insights into Its Relationship with Vegetation Cover

Accurate and precise prediction of actual evapotranspiration (AET) on a large scale is a fundamental issue in natural sciences such as forestry (especially in species selection and planning), hydrology, and agriculture. With the estimation of AET, controlling dams, agriculture, and irrigation and providing potable and utility water supply for industry would be possible. Gathering reliable AET data is possible only with a sufficient weather station network, which is rarely established in many countries like Turkey. Therefore, climate models must be developed for reliable AET data, especially in countries with complex terrains. This study aimed to generate spatiotemporal AET surfaces using the Australian National University spline (ANUSPLIN) model and compare the results with the maps generated by the inverse distance weighting (IDW) and co-kriging (KRG) interpolation techniques. Findings from the interpolated surfaces were validated in three ways: (1) some diagnostics from the surface fitting model include measures such as signal, mean, root mean square predictive error, root mean square error estimate, root mean square residual of the spline, and the estimated standard deviation of noise in the spline; (2) a comparison of common error statistics between the interpolated surfaces and withheld climate data; and (3) evaluation by comparing model results with other interpolation methods using metrics such as mean absolute error, mean error, root mean square error, and adjusted R2 (R2adj). The correlation between AET and normalized difference vegetation index (NDVI) was also evaluated. ANUSPLIN outperformed the other techniques, accounting for 73 to 94% (RMSE: 3.7 to 26.1%) of the seasonal variation in AET with an annual value of 83% (RMSE: 10.0%). The correlation coefficient between observed and predicted AET based on NDVI ranged from 0.49 to 0.71 for point-based and 0.62 to 0.83 for polygon-based data. The generated maps at a spatial resolution of 0.005° × 0.005° could provide valuable insights to researchers and practitioners in the natural resources management domain.

Observing kinematic anisotropies of the stochastic background with LISA

We propose a diagnostic tool for future analyses of stochastic gravitational wave background signals of extra-galactic origin in LISA data. Next-generation gravitational wave detectors hold the capability to track unresolved gravitational waves bundled into a stochastic background. This composite background contains cosmological and astrophysical contributions, the exploration of which offers promising avenues for groundbreaking new insights into very early universe cosmology as well as late-time structure formation. In this article, we develop a full end-to-end pipeline for the extraction of extra-galactic signals, based on kinematic anisotropies arising from the galactic motion, via full-time-domain simulations of LISA's response to the gravitational wave anisotropic sky. Employing a Markov-Chain-Monte-Carlo map-making scheme, multipoles up to ℓ=2 are recovered for scale-free spectra in the case of a high signal-to-noise ratio. We demonstrate that our analysis is consistently beating sample variance and is robust against statistical and systematic errors. The impact of instrumental noise on the extraction of kinematic anisotropies is investigated, and we establish a detection threshold of Ω GW ≳ 5 × 10-8 in the presence of instrument-induced noise. Potential avenues for improvement in our methodology are highlighted.