Interval Width Research Articles

First-passage time of a Brownian searcher with stochastic resetting to random positions.

We study the effect of a resetting point randomly distributed around the origin on the mean first-passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin and find that the mean first-passage time of the latter can be larger or smaller than the distributed case, depending on whether the resetting points are symmetrically or asymmetrically distributed. In particular, we prove the existence of an optimal reset rate that minimizes the mean first-passage time for distributed resetting to a finite interval if the target is located outside this interval. When the target position belongs to the resetting interval or it is infinite then no optimal reset rate exists, but there is an optimal resetting interval width or resetting characteristic scale which minimizes the mean first-passage time. We also show that the first-passage density averaged over the resetting points depends on its first moment only. As a consequence, there is an equivalent point such that the first-passage problem with resetting to that point is statistically equivalent to the case of distributed resetting. We end our study by analyzing the fluctuations of the first-passage times for these cases. All our analytical results are verified through numerical simulations.

Measuring the variability of personality traits with interval responses: Psychometric properties of the dual-range slider response format

Measuring the variability in persons’ behaviors and experiences using ecological momentary assessment is time-consuming and costly. We investigate whether interval responses provided through a dual-range slider (DRS) response format can be used as a simple and efficient alternative: Respondents indicate variability in their behavior in a retrospective rating by choosing a lower and an upper bound on a continuous, bounded scale. We investigate the psychometric properties of this response format as a prerequisite for further validation. First, we assess the test–retest reliability of factor-score estimates for the width of DRS intervals. Second, we test whether factor-score estimates of the visual analog scale (VAS) and the location of DRS intervals show convergent validity. Third, we investigate whether factor-score estimates for the DRS are uncorrelated between different personality scales. We present a longitudinal multitrait-multimethod study using two personality scales (Extraversion, Conscientiousness) and two response formats (VAS, DRS) at two measurement occasions (6–8 weeks apart) for which we estimate factor-score correlations in a joint item response theory model. The test–retest reliability of the width of DRS intervals was high (ρ^≥.73\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .73$$\\end{document}). Also, convergent validity between location scores of VAS and DRS was high (ρ^≥.88\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .88$$\\end{document}). Conversely, discriminant validity of the width of DRS intervals between Extraversion and Conscientiousness was poor (ρ^≥.94\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{\\rho } \\ge .94$$\\end{document}). In conclusion, the DRS seems to be a reliable response format that could be used to measure the central tendency of a trait equivalently to the VAS. However, it might not be well suited for measuring intra-individual variability in personality traits.

Stability of Cauchy horizon in charged black holes surrounded by quintessential dark energy

By investigating the Quasinormal Modes of a massless neutral scalar field, we have explored the influence of dark energy on the strong cosmic censorship (SCC) of charged de Sitter-like black holes. The results indicate that SCC can consistently be violated as long as the black hole approaches extremality. However, as the state parameter σ=3ωf+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma = 3\\omega _f + 1$$\\end{document} of the dark energy increases and approaches zero, the width of SCC violation interval demonstrates an overall decreasing trend, converging towards zero. Specifically, our research has identified a critical state parameter σcrt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{\ ext {crt}}$$\\end{document} for dark matter. Beyond this critical value, enhancing the state parameter effectively mitigates SCC violations. However, at this critical threshold, the width of the violation interval stabilizes or marginally increase. These findings reveal a nuanced relationship between the asymptotic properties of black holes and the validity of the SCC, offering profound insights into potential mechanisms governing both the occurrence and alleviation of SCC violations.

Comparison of the applicability of seven calculation equations of glomerular filtration rate among elderly people in China

BackgroundAt present, estimated glomerular filtration rate (eGFR) remains the most frequently utilized parameter in the evaluation of kidney injury severity. Numerous equations have been formulated based on serum creatinine (Scr) or serum cystatin C (Cysc) levels. However, there is a lack of consensus regarding the efficacy of these equations in assessing eGFR, particularly for elderly individuals in China. This study aimed to evaluate the applicability of the MDRD, MDRDc, CKD-EPI series, BIS1, and FAS equations within the Chinese elderly population.MethodsA cohort of 298 elderly patients with measured GFR (mGFR) was enrolled. The patients were categorized into three subgroups based on their mGFR levels. The eGFR performance was examined, taking into account bias, interquartile range (IQR), accuracy P30, and root-mean-square error (RMSE). Bland–Altman plots were employed to verify the validity of eGFR.ResultsThe participants had a median age of 71 years, with 167 (56.0%) being male. Overall, no significant differences in bias were observed among the seven equations (P > 0.05). In terms of IQR, P30, and RMSE, the BIS1 equation demonstrated superior accuracy (14.61, 72.1%, and 13.53, respectively). When mGFR < 30 ml/min/1.73 m2, all equations underestimated the true GFR, with the highest accuracy reaching only 59%. Bland–Altman plots indicated that the BIS1 equation exhibited the highest accuracy, featuring a 95% confidence interval (CI) width of 52.37.ConclusionsThis study suggested that the BIS1 equation stands out as the most applicable for estimating GFR in Chinese elderly patients with normal renal function or only moderate decline. 2020NL-085-03, 2020.08.10, retrospectively registered.

A novel combined wind speed forecasting system based on fuzzy granulation and multi-objective optimization

With the increasing application of wind energy, reliable wind speed prediction has become imperative. However, prior studies predominantly concentrated on single-model predictions, disregarding the inherent uncertainty in wind speed. This oversight resulted in inadequate deterministic and probabilistic forecasting outcomes across varying scenarios. To make up for these shortcomings, a novel forecasting system combining a data preprocessing technique, a sub-model selection method, and a modified multi-objective integrate optimization strategy is designed in this paper. According to the data obtained from China's wind farm, the forecasting efficiency of this system is verified from multiple perspectives. The findings show that the system takes advantage of each model to boost the precision and stability of point prediction successfully. Furthermore, it achieves higher interval coverage and narrower interval width under distinct confidence levels. These results highlight the system's potential as a reliable technical support for efficient dispatching of the entire power system.

Sample size determination for interval estimation of the prevalence of a sensitive attribute under non-randomized response models.

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.

A Confidence Interval for the Difference Between Standardized Regression Coefficients

Researchers are often interested in comparing predictors, a practice commonly done via informal comparisons of standardized regression slopes. However, formal interval-based approaches offer advantages over informal comparison. Specifically, this article examines a delta-method-based confidence interval for the difference between two standardized regression coefficients, building upon previous work on confidence intervals for single coefficients. Using Monte Carlo simulation studies, the proposed approach is evaluated at finite sample sizes with respect to coverage rate, interval width, Type I error rate, and statistical power under a variety of conditions, and is shown to outperform an alternative approach that uses the standard covariance matrix found in regression textbooks. Additional simulations evaluate current software implementations, small sample performance, and multiple comparison procedures for simultaneously testing multiple differences of interest. Guidance on sample size planning for narrow confidence intervals, an R function to conduct the proposed method, and two empirical demonstrations are provided. The goal is to offer researchers a different tool in their toolbox for when comparisons among standardized coefficients are desired, as a supplement to, rather than a replacement for, other potentially useful analyses.

Beyond mirkwood: Enhancing SED Modeling with Conformal Predictions

Traditional spectral energy distribution (SED) fitting techniques face uncertainties due to assumptions in star formation histories and dust attenuation curves. We propose an advanced machine learning-based approach that enhances flexibility and uncertainty quantification in SED fitting. Unlike the fixed NGBoost model used in mirkwood, our approach allows for any scikit-learn-compatible model, including deterministic models. We incorporate conformalized quantile regression to convert point predictions into error bars, enhancing interpretability and reliability. Using CatBoost as the base predictor, we compare results with and without conformal prediction, demonstrating improved performance using metrics such as coverage and interval width. Our method offers a more versatile and accurate tool for deriving galaxy physical properties from observational data.

Comparison of statistical methods used to meta-analyse results from interrupted time series studies: an empirical study

BackgroundThe Interrupted Time Series (ITS) is a robust design for evaluating public health and policy interventions or exposures when randomisation may be infeasible. Several statistical methods are available for the analysis and meta-analysis of ITS studies. We sought to empirically compare available methods when applied to real-world ITS data.MethodsWe sourced ITS data from published meta-analyses to create an online data repository. Each dataset was re-analysed using two ITS estimation methods. The level- and slope-change effect estimates (and standard errors) were calculated and combined using fixed-effect and four random-effects meta-analysis methods. We examined differences in meta-analytic level- and slope-change estimates, their 95% confidence intervals, p-values, and estimates of heterogeneity across the statistical methods.ResultsOf 40 eligible meta-analyses, data from 17 meta-analyses including 282 ITS studies were obtained (predominantly investigating the effects of public health interruptions (88%)) and analysed. We found that on average, the meta-analytic effect estimates, their standard errors and between-study variances were not sensitive to meta-analysis method choice, irrespective of the ITS analysis method. However, across ITS analysis methods, for any given meta-analysis, there could be small to moderate differences in meta-analytic effect estimates, and important differences in the meta-analytic standard errors. Furthermore, the confidence interval widths and p-values for the meta-analytic effect estimates varied depending on the choice of confidence interval method and ITS analysis method.ConclusionsOur empirical study showed that meta-analysis effect estimates, their standard errors, confidence interval widths and p-values can be affected by statistical method choice. These differences may importantly impact interpretations and conclusions of a meta-analysis and suggest that the statistical methods are not interchangeable in practice.

Forming Control via Interval Width in Directed Energy Deposition-Arc Process

A novel controller, employing a variable-structure single-neuron adaptive PSD (proportional integral derivative) approach, was proposed for regulating the deposition width variation in the Directed Energy Deposition-Arc (DED-Arc) layer. During experimental trials, the deposition speed was chosen as the manipulated variable, while the width of the deposition layer served as the measured parameter. To facilitate controller design, a vision sensor was custom-designed to accurately detect the width of the deposition layer. The captured image of the deposition layer’s dimensions enabled the precise determination of the deposited thickness, forming the basis for subsequent controller development. In performance assessments, deliberate interference was intentionally introduced into the deposition current, deposition layer height, and the targeted deposition layer width. The assessment involved the controlled deposition of ten-layer components, focusing on width regulation for each deposition layer. The results demonstrate that the proposed controller significantly enhances the deposition process stability, particularly within a range of desired deposition widths from 7.5 mm to 8.3 mm.

Reliability generalization meta-analysis: comparing different statistical methods

AbstractReliability generalization (RG) is a kind of meta-analysis that aims to characterize how reliability varies from one test application to the next. A wide variety of statistical methods have typically been applied in RG meta-analyses, regarding statistical model (ordinary least squares, fixed-effect, random effects, varying-coefficient models), weighting scheme (inverse variance, sample size, not weighting), and transformation method (raw, Fisher’s Z, Hakstian and Whalen’s and Bonett’s transformation) of reliability coefficients. This variety of methods compromise the comparability of RG meta-analyses results and their reproducibility. With the purpose of examining the influence of the different statistical methods applied, a methodological review was conducted on 138 published RG meta-analyses of psychological tests, amounting to a total of 4,350 internal consistency coefficients. Among all combinations of procedures that made theoretical sense, we compared thirteen strategies for calculating the average coefficient, eighteen for calculating the confidence intervals of the average coefficient and calculated the heterogeneity indices for the different transformations of the coefficients. Our findings showed that transformation methods of the reliability coefficients improved the normality adjustment of the coefficient distribution. Regarding the average reliability coefficient and the width of confidence intervals, clear differences among methods were found. The largest discrepancies were found between the different strategies for calculating confidence intervals. Our findings point towards the need for the meta-analyst to justify the statistical model assumed, as well as the transformation method of the reliability coefficients and the weighting scheme.

ForecastNet Wind Power Prediction Based on Spatio-Temporal Distribution

The integration of large-scale wind power into the power grid threatens the stable operation of the power system. Traditional wind power prediction is based on time series without considering the variability between wind turbines in different locations. This paper proposes a wind power probability density prediction method based on a time-variant deep feed-forward neural network (ForecastNet) considering a spatio-temporal distribution. First, the outliers in the wind turbine data are detected based on the isolated forest algorithm and repaired through Lagrange interpolation. Then, based on the graph attention mechanism, the features of the proximity node information of the individual wind turbines in the wind farm are extracted and the input feature matrix is constructed. Finally, the wind power probability density prediction results are obtained using the ForecastNet model based on three different hidden layer variants. The experimental results show that the ForecastNet model with a hidden layer as a dense network based on the attention mechanism (ADFN) predicts better. The average width of the prediction intervals at achieved confidence levels for all interval coverage is reduced by 34.19%, 35.41%, and 35.17%, respectively, when compared to the model with the hidden layer as a multilayer perceptron. For different categories of wind turbines, ADFN also achieves relatively narrow interval average widths of 368.37 kW, 315.87 kW, and 299.13 kW, respectively.

Interval estimation of relative risks for combined unilateral and bilateral correlated data

ABSTRACT Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

Conformal prediction of option prices

The uncertainty associated with option price predictions has largely been overlooked in the literature. This paper aims to fill this gap by quantifying such uncertainty using conformal prediction. Conformal prediction is a model-agnostic procedure that constructs prediction intervals, ensuring valid coverage in finite samples without relying on distributional assumptions. Through the simulation of synthetic option prices, we find that conformal prediction generates prediction intervals for gradient boosting machines with an empirical coverage close to the nominal level. Conversely, non-conformal prediction intervals exhibit empirical coverage levels that fall short of the nominal target. In other words, they fail to contain the actual option price more frequently than expected for a given coverage level. As anticipated, we also observe a decrease in the width of prediction intervals as the size of the training data increases. However, we uncover significant variations in the width of these intervals across different options. Specifically, out-of-the-money options and those with a short time-to-maturity exhibit relatively wider prediction intervals. Then, we perform an empirical study using American call and put options on individual stocks. We find that the empirical results replicate those obtained in the simulation experiment.

A novel demand response-based distributed multi-energy system optimal operation framework for data centers

To address the increasing energy demands in data centers, distributed multi-energy system (DMES) can provide an efficient solution. This study proposes a DMES coupled by photovoltaics, wind turbines, ground source heat pump, internal combustion engines, electric chillers, absorption chillers, and energy storage device. The optimal scheduling of DMES with source-load interaction plays a crucial role in improving the performance of data centers. To achieve this, an integrated demand response (IDR) strategy is established, considering time-of-use pricing and renewable energy peak subsidies. Then, a clean and economical optimal operation model for DMES based on proposed IDR strategy and carbon trading mechanisms is established. Furthermore, to enhance the robustness of scheduling, this study analyzes the impacts of uncertainties in renewable energy output and demand response on DMES operation using the Monte Carlo method and interval method. Case study results demonstrate that the proposed IDR strategy increases electricity and cooling loads while reducing heat loads during the peak period of renewable energy generation, compared to the traditional IDR strategy. The proposed scheduling model, which incorporates the proposed IDR strategy and carbon trading mechanism, improves data center performance by reducing total costs by 1.85%, carbon emissions by 0.56%, electricity purchases by 2.93%, while increasing renewable energy utilization by 0.77%. The results also highlight the critical role of energy storage devices, with an optimal initial charge state is 0.5. Additionally, optimization considering multiple uncertainties, results in higher total costs and broader interval widths compared to single-factor uncertainty optimization, but reduces system operational risk.

Reliability-based journey time prediction via two-stream deep learning with multi-source data

This paper presents a distribution-free reliability-based prediction approach for estimating journey time intervals with multi-source data using a two-stream deep learning framework. The prediction framework consists of a long short-term memory (LSTM) module for extracting temporal features and a convolutional neural network (CNN) module for extracting spatial-temporal features from the heterogeneous data. The precision and reliability of the prediction are assessed respectively by the Mean Prediction Interval Width (MPIW) and Prediction Interval Coverage Probability (PICP) metrics. For computational effectiveness, a Gaussian approximation is adopted to formulate a smooth and differentiable loss function for training the prediction framework. The computational experiments are conducted based on a real-world Hong Kong corridor, where multi-source data including traffic and weather conditions are collected. The proposed framework shows significant improvements over existing methods in terms of both precision and reliability over a range of traffic and weather conditions. This study contributes to the development of reliability-based intelligent transportation systems with advanced deep learning techniques.

Interval estimates of total content of antioxidants for different analytical assays

Determination of total content (сΣ) of similar analytes recalculated to the standard substance Xst is a commonly used but metrologically incorrect measuring procedure leading to significant systematic errors (B-type uncertainties). Interval estimate сΣ is an alternative method (V.I. Vershinin et al., 2016) not requiring recalculation to Xst and, in difference from calculating total indices, not depending on the nature and ratio of the sought group constituents present in the sample. Such estimates are used for evaluating total content of antioxidants (AO) in foodstuffs. However, the dependence of these estimates on the choice of group reagent and signal measuring procedure is uncertain. To address this question, model mixtures of AO with known сΣ values ranging from 10–5 to 10–4 mol/L were prepared and examined. Generalized signals were measured spectrophotometrically using Folin-Ciocalteu (F-C) and FRAP methods, and traditional and interval estimates of сΣ were calculated and compared. The true values of сΣ were within the respective intervals for all model mixtures; in case of F-C method the intervals were wider and shifted towards higher сΣ values. The FRAP procedure was modified by using AO-concentrations in mol-eq/L, reducing the reaction time and substituting the auxiliary reagent. This modification successfully leveled the sensibility coefficients of individual AOs and made the relative width of intervals three times as narrower. Modified FRAP method was used for group analysis of wines, black tea infusions and juices. Corresponding interval estimates of сΣ were obtained and compared. Unresolved issues and future research directions related to interval estimates are discussed.

Uncertainty quantification in neural-network based pain intensity estimation.

Improper pain management leads to severe physical or mental consequences, including suffering, a negative impact on quality of life, and an increased risk of opioid dependency. Assessing the presence and severity of pain is imperative to prevent such outcomes and determine the appropriate intervention. However, the evaluation of pain intensity is a challenging task because different individuals experience pain differently. To overcome this, many researchers in the field have employed machine learning models to evaluate pain intensity objectively using physiological signals. However, these efforts have primarily focused on pain point estimation, disregarding inherent uncertainty and variability in the data and model. A point estimate, which provides only partial information, is not sufficient for sound clinical decision-making. This study proposes a neural network-based method for objective pain interval estimation, and quantification of uncertainty. Our approach, which enables objective pain intensity estimation with desired confidence probabilities, affords clinicians a better understanding of a person's pain intensity. We explored three distinct algorithms: the bootstrap method, lower and upper bound estimation (LossL) optimized by genetic algorithm, and modified lower and upper bound estimation (LossS) optimized by gradient descent algorithm. Our empirical results demonstrate that LossS outperforms the other two by providing narrower prediction intervals. For 50%, 75%, 85%, and 95% prediction interval coverage probability, LossS provides average interval widths that are 22.4%, 7.9%, 16.7%, and 9.1% narrower than those of LossL, and 19.3%, 21.1%, 23.6%, and 26.9% narrower than those of bootstrap. As LossS outperforms, we assessed its performance in three different model-building approaches: (1) a generalized approach using a single model for the entire population, (2) a personalized approach with separate models for each individual, and (3) a hybrid approach with models for clusters of individuals. Results demonstrate that the hybrid model-building approach provides the best performance.

An elaboration on sample size determination for correlations based on effect sizes and confidence interval width: a guide for researchers.

This paper aims to serve as a useful guide for sample size determination for various correlation analyses that are based on effect sizes and confidence interval width. Sample size determinations are calculated for Pearson's correlation, Spearman's rank correlation, and Kendall's Tau-b correlation. Examples of sample size statements and their justification are also included. Using the same effect sizes, there are differences between the sample size determination of the 3 statistical tests. Based on an empirical calculation, a minimum sample size of 149 is usually adequate for performing both parametric and non-parametric correlation analysis to determine at least a moderate to an excellent degree of correlation with acceptable confidence interval width. Determining data assumption(s) is one of the challenges to offering a valid technique to estimate the required sample size for correlation analyses. Sample size tables are provided and these will help researchers to estimate a minimum sample size requirement based on correlation analyses.

Application of Helium-Based oscillating heat pipes in cryogenic superconducting system

Copper is the cooling transfer material used in cryogenic superconducting systems. Its effective thermal conductivity (ETC) in the 4 K region is only 400 W·m−1·K−1, which leads to disadvantages such as large temperature differences and delayed temperature fluctuation. These restrict the improvement of the cooling performance of superconducting magnets. Oscillating heat pipe (OHP) has an ETC of two orders higher than copper, but it is unknown whether the heat generated by superconducting magnets excites OHP to produce oscillatory behavior. It limited its application in superconducting systems. In this study, the structure of helium-based OHP is designed, the heat transfer performance test rig in the 4 K region is constructed, and the numerical simulation method of the gas–liquid two-phase flow and heat transfer process of OHP is built. The oscillating power interval including the trigger power, the dryout power, the width of the power interval, and the optimal heating power is obtained with the heating power is 0.05 W ∼ 1 W, the liquid filling ratio is 10 %-90 % and the turns is 1–6. And the change rule of oscillating power interval is revealed. The research results provide reliable data for the application of helium-based OHP in cryogenic superconducting systems.