Reliable Confidence Intervals Research Articles

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Reliability evaluation in the zero‐failure Weibull case based on double‐modified hierarchical Bayes

AbstractHierarchical Bayes, or E‐Bayes, is frequently used to estimate the failure probability when solving a zero‐failure reliability evaluation model; however, the accuracy of the reliability estimation using these methods is not very good in practice. Due to this, a novel double‐modified hierarchical Bayes (DMH‐Bayes) is proposed for Weibull characteristic data in this study to enhance failure probability estimation and improve reliability point estimation accuracy. Meanwhile, in order to guarantee the preservation of the assessment findings' consistency and confidence level, the parametric Bootstrap method (P‐Bootstrap) and the L‐moment estimation method based on point estimation are introduced to obtain reliability confidence interval estimates. Based on Monte–Carlo simulation testing and analysis of a gyroscope bearing, the new model is confirmed to have better applicability and robustness while improving the accuracy of reliability assessment.

A novel SCNN-LSTM model for predicting the SNR confidence interval in wearable wireless sensor network

Accurate real-time prediction of link quality is crucial for enhancing the reliable responsiveness of wearable devices within Wireless Wearable Sensor Networks (WWSNs). Specifically, the Signal-to-Noise Ratio (SNR), a pivotal parameter for predicting link quality, exhibits complex temporal characteristics influenced by stochastic and non-stochastic factors. To improve the accuracy of link quality prediction in WWSNs, we aim to explore a novel predictive model, introducing a filtering layer that seeks to enhance the precision of predicting upper and lower boundaries of link reliability confidence intervals. First, we adopt the SNR time series as the evaluation metric and decompose the SNR sequences into time-varying and stochastic standard deviation sequences by wavelet decomposition. Subsequently, we propose an innovative SCNN-LSTM model, incorporating the SincNet filtering layer to extract specific frequency components from the input SNR sequences. Afterward, integrating standard deviation sequences, the model predicts upper and lower boundaries of link reliability confidence intervals. Finally, we conduct the validation experiments on the public dataset LightGBM-LQP and our WWSN dataset Basketball shot. Compared to BPNN, ARIMA, and WNN, the evaluation matrices of MAE, RMSE, R2 in SCNN-LSTM have been improved, and the deviation between the predicted standard deviation and the actual standard deviation has reached the minimum of 0.1. The results demonstrate that SCNN-LSTM outperforms classical prediction models in predicting upper and lower limits of link reliability confidence intervals in WWSNs.

Natural Gradient Boosting for Probabilistic Prediction of Soaked CBR Values Using an Explainable Artificial Intelligence Approach

The California bearing ratio (CBR) value of subgrade is the most used parameter for dimensioning flexible and rigid pavements. The test for determining the CBR value is typically conducted under soaked conditions and is costly, labour-intensive, and time-consuming. Machine learning (ML) techniques have been recently implemented in engineering practice to predict the CBR value from the soil index properties with satisfactory results. However, they provide only deterministic predictions, which do not account for the aleatoric uncertainty linked to input variables and the epistemic uncertainty inherent in the model itself. This work addresses this limitation by introducing an ML model based on the natural gradient boosting (NGBoost) algorithm, becoming the first study to estimate the soaked CBR value from this probabilistic perspective. A database of 2130 soaked CBR tests was compiled for this study. The NGBoost model showcased robust predictive performance, establishing itself as a reliable and effective algorithm for predicting the soaked CBR value. Furthermore, it produced probabilistic CBR predictions as probability density functions, facilitating the establishment of reliable confidence intervals, representing a notable improvement compared to conventional deterministic models. Finally, the Shapley additive explanations method was implemented to investigate the interpretability of the proposed model.

Bootstrapping for parameter uncertainty in the space–time epidemic-type aftershock sequence model

SUMMARY This paper proposes the use of the parametric bootstrap as a simple way of obtaining reliable confidence intervals for the parameters in the space–time epidemic-type aftershock sequence (ETAS) model. Using an earthquake data catalogue spanning almost 20 yr of seismic activity in the Pacific Ocean off the shores of Vancouver Island (British Columbia, Canada), the authors show through simulation that the confidence intervals based on asymptotic maximum-likelihood theory can sometimes be misleading. In contrast, confidence intervals based on empirical quantiles from bootstrap samples have reliable nominal coverage, provided that edge effects are properly taken into account, both in the bootstrap procedure and in simulation studies. An R package called ETASbootstrap, developed by the authors, facilitates the use of this resampling procedure.

Software testing and release decision at different statistical confidence levels with consideration of debuggers’ learning and negligent factors

This research delves into the software testing process and its environmental factors to uncover the core elements influencing software reliability. Specifically, it focuses on the learning and negligent aspects of the software reliability growth model. The learning factor accelerates reliability growth, leading to an S-shaped curve in the mean value function, while the negligent factor highlights the occurrence of imperfect debugging. The study also uses Brownian motion and stochastic differential equations to establish statistical confidence intervals for reliability and costs. These intervals aid software managers in assessing potential release risks at various confidence levels, allowing them to make informed decisions considering resource constraints and desired system reliability levels across different scenarios.

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided.

Probabilistic Shear Strength Prediction for Deep Beams Based on Bayesian-Optimized Data-Driven Approach

To ensure the safety of buildings, accurate and robust prediction of a reinforced concrete deep beam’s shear capacity is necessary to avoid unpredictable accidents caused by brittle failure. However, the failure mechanism of reinforced concrete deep beams is very complicated, has not been fully elucidated, and cannot be accurately described by simple equations. To solve this issue, machine learning techniques have been utilized and corresponding prediction models have been developed. Nevertheless, these models can only provide deterministic prediction results of the scalar type, and the confidence level is uncertain. Thus, these prediction results cannot be used for the design and assessment of deep beams. Therefore, in this paper, a probabilistic prediction approach of the shear strength of reinforced concrete deep beams is proposed based on the natural gradient boosting algorithm trained on a collected database. A database of 267 deep beam experiments was utilized, with 14 key parameters identified as the inputs related to the beam geometry, material properties, and reinforcement details. The proposed NGBoost model was compared to empirical formulas from design codes and other machine learning methods. The results showed that the NGBoost model achieved higher accuracy in mean shear strength prediction, with an R2 of 0.9045 and an RMSE of 38.8 kN, outperforming existing formulas by over 50%. Additionally, the NGBoost model provided probabilistic predictions of shear strength as probability density functions, enabling reliable confidence intervals. This demonstrated the capability of the data-driven NGBoost approach for robust shear strength evaluation of RC deep beams. Overall, the results illustrated that the proposed probabilistic prediction approach dramatically surpassed the current formulas adopted in design codes and machine learning models in both prediction accuracy and robustness.

Approaches to improve and adapt maternal mortality estimations in low- and middle-income countries: A scoping review.

In the absence of robust vital registration systems, many low- and middle-income countries (LMICs) rely on national surveys or routine surveillance systems to estimate the maternal mortality ratio (MMR). Although the importance of MMR estimates in ending preventable maternal deaths is acknowledged, there is limited research on how different approaches are used and adapted, and how these adaptations function. To assess methods for estimating maternal mortality in LMICs and the rationale for these modifications. A literature search with the terms "maternal death", "surveys" and "low- and middle-income countries" was performed in Medline, Embase, Web of Science, Scopus, CINAHL, APA PsycINFO, ERIC, and IBSS from January 2013 to March 17, 2023. Studies were eligible if their main focus was to compare, adapt, or assess methods to estimate maternal mortality in LMICs. Titles and abstracts were screened using Rayyan. Relevant articles were independently reviewed by two reviewers against inclusion criteria. Data were extracted on mortality measurement methods, their context, and results. Nineteen studies were included, focusing on data completeness, subnational estimates, and community involvement. Routinely generated MMR estimates are more complete when multiple data sources are triangulated, including data from public and private health facilities, the community, and local authorities (e.g. vital registration, police reports). For subnational estimates, existing (e.g. the sisterhood method and reproductive-age mortality surveys [RAMOS]) and adapted methods (e.g. RAMOS 4 + 2 and Pictorial Sisterhood Method) provided reliable confidence intervals. Community engagement in data collection increased community awareness of maternal deaths, provided local ownership, and was expected to reduce implementation costs. However, most studies did not include a cost-effectiveness analysis. Household surveys with community involvement and RAMOS can be used to increase data validity, improve local awareness of maternal mortality estimates, and reduce costs in LMICs.

Structural VAR models in the Frequency Domain

This paper proposes a joint methodology for the identification and inference of structural vector autoregressive models in the frequency domain. We show that identifying restrictions can be written naturally as an asymptotic least squares problem (Gouriéroux et al., 1985) in which there is a continuum of nonlinear estimating equations. Following Carrasco and Florens (2000), we then propose a continuum asymptotic least squares estimator (C-ALS) that efficiently exploits the continuum of estimating equations, thereby allowing to obtain optimal consistent estimates of impulse responses and reliable confidence intervals. Moreover, the identifying restrictions can be formally tested using an appropriate J-stat, and the frequency band can be selected using a data-driven procedure. Finally, we provide some Monte Carlo simulations and an application regarding the hours–productivity debate.

The Importance of Fructosamine for Monitoring the Compensation and Effectiveness of Diabetes Treatment.

The use of fructosamine to assess the glycemic control represents a new step in diagnostics, and it has been accompanied by the active scientific discussion in recent years. That is why the purpose of this work is to study the average level of fructosamine in apparently healthy individuals and individuals with diabetes mellitus (DM), as well as the possibility to use it when evaluating the effectiveness of inpatient treatment of patients with hyperglycemia on the seven to ten days of hospitalization. This research work was carried out in Alma-Ata, Republic of Kazakhstan, based on the endocrinology department in the period from 2020 to 2022. The work consists of a retrospective analysis of previously examined patients and a prospective stage. The statistical evaluation was carried out with the calculation of reliability coefficient, confidence interval, and criteria for testing for normality. The level of fructosamine in healthy individuals in the corresponding region was analyzed in this article for the first time, and the correlation between this indicator and the level of glycated hemoglobin was found. The effectiveness of treatment of the Type 2 DM (according to the treatment protocol) has also been studied in stationary conditions for the seven to ten days, which makes it possible to judge the effectiveness of the prescribed therapy. These results will allow identifying the irrationality of the prescribed therapy at an early stage, which is especially important for the correct management of patients with this pathology, and minimizing the possible complications.

Lemon: LEns MOdelling with Neural networks – I. Automated modelling of strong gravitational lenses with Bayesian Neural Networks

ABSTRACT The unprecedented number of gravitational lenses expected from new-generation facilities such as the ESA Euclid telescope and the Vera Rubin Observatory makes it crucial to rethink our classical approach to lens-modelling. In this paper, we present lemon (Lens Modelling with Neural networks): a new machine-learning algorithm able to analyse hundreds of thousands of gravitational lenses in a reasonable amount of time. The algorithm is based on a Bayesian Neural Network: a new generation of neural networks able to associate a reliable confidence interval to each predicted parameter. We train the algorithm to predict the three main parameters of the singular isothermal ellipsoid model (the Einstein radius and the two components of the ellipticity) by employing two simulated data sets built to resemble the imaging capabilities of the Hubble Space Telescope and the forthcoming Euclid satellite. In this work, we assess the accuracy of the algorithm and the reliability of the estimated uncertainties by applying the network to several simulated data sets of 104 images each. We obtain accuracies comparable to previous studies present in the current literature and an average modelling time of just ∼0.5 s per lens. Finally, we apply the lemon algorithm to a pilot data set of real lenses observed with HST during the SLACS program, obtaining unbiased estimates of their SIE parameters. The code is publicly available on GitHub (https://github.com/fab-gentile/LEMON).

Eye symptoms due to environmental and climatic parameters variation: The Google trends and eye-drops selling as monitors

Climate and pollution challenges have been increasing over the last decades. The eyes are susceptible to those challenges. Modern life allows the population to search internet engine tools for information regarding eye symptoms. Drug sales are globally monitored to orient the actions of pharmaceutical companies. Monitoring those two big data sources of information (i.e., trends in internet search of eye diseases and symptoms and eye drop sales) can be correlated with climate and pollution data of the same locations and time to create standards capable of alerting about climate and pollution challenges. The present hypothesis is that climate and pollution level changes correlate with an increase in the search for ocular discomfort on the internet and the sales volume of symptomatic-relieving eye drops, providing a new tool to people’s health and preventive medicine. The potential correlation with statistical significance and a reliable confidence interval will allow using these correlations as tools to monitor remotely and to compare the parameters among different regions and over time. The benefits are to provide subsidies to public health strategies to predict and minimize climatic and environmental parameters effects.

Stress–Strength Inference on the Multicomponent Model Based on Generalized Exponential Distributions under Type-I Hybrid Censoring

The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation methods of the maximum likelihood and Bayesian are utilized to infer the system reliability. For the Bayesian estimation method, informative and non-informative priors combined with three loss functions are considered. Because the computational difficulty on working posteriors, the Markov chain Monte Carlo method is adopted to obtain the approximation of the reliability estimator posterior. In addition, the bootstrap method and highest probability density interval are used to obtain the reliability confidence intervals. The simulation study shows that the Bayes estimator with informative prior is superior to other competitors. Finally, two real examples are given to illustrate the proposed estimation methods.

Mastering uncertainty in performance estimations of configurable software systems

Understanding the influence of configuration options on the performance of a software system is key for finding optimal system configurations, system understanding, and performance debugging. In the literature, a number of performance-influence modeling approaches have been proposed, which model a configuration option’s influence and a configuration’s performance as a scalar value. However, these point estimates falsely imply a certainty regarding an option’s influence that neglects several sources of uncertainty within the assessment process, such as (1) measurement bias, choices of model representation and learning process, and incomplete data. This leads to the situation that different approaches and even different learning runs assign different scalar performance values to options and interactions among them. The true influence is uncertain, though. There is no way to quantify this uncertainty with state-of-the-art performance modeling approaches.We propose a novel approach, P4, which is based on probabilistic programming, that explicitly models uncertainty for option influences and consequently provides a confidence interval for each prediction alongside a scalar. This way, we can explain, for the first time, why predictions may be erroneous and which option’s influence may be unreliable. An evaluation on 13 real-world subject systems shows that P4’s accuracy is in line with the state of the art while providing reliable confidence intervals, in addition to scalar predictions. We qualitatively explain how uncertain influences of individual options and interactions cause inaccurate predictions.

Inter-rater and intra-rater reliability of isotonic exercise monitoring device for measuring active knee extension.

The goal of this study was to assess the reliability of electromyography and range of motion measurements obtained using a knee exercise monitoring system. This device was developed to collect data on knee exercise activities. Twenty healthy individuals performed isotonic quadriceps exercises in this study. The vastus medialis surface electromyography (sEMG) and range of motion (ROM) of the knee were recorded during the exercise using the isotonic knee exercise monitoring device, the Mobi6-6b, and a video camera system. Each subject underwent a second measuring session at least 24 h after the first session. To determine reliability, the intraclass correlation coefficients (ICCs) and standard error of measurement (SEM) at the 95% confidence interval were calculated, and a Bland-Altman analysis was performed. For inter-rater reliability, the ICCs of the mean absolute value (MAV) and root mean square (RMS) of sEMG were 0.73 (0.49, 0.86) and 0.79 (0.61, 0.89), respectively. ROM had an ICC of 0.93 (0.02, 0.98). The intra-rater reliability of the MAV of the sEMG was 0.89 (0.71, 0.96) and the intra-rater reliability of RMS of the sEMG was 0.88 (0.70, 0.95). The ROM between days had an intra-rater reliability of 0.82 (0.54, 0.93). The Bland-Altman analysis demonstrated no systematic bias in the MAV and RMS of sEMG, but revealed a small, systematic bias in ROM (-0.8311 degrees). For sEMG and range of motion measures, the isotonic knee exercise monitoring equipment revealed moderate to excellent inter- and intra-rater agreement. However, the confidence interval of ROM inter-rater reliability was quite large, indicating a small agreement bias; hence, the isotonic knee exercise monitor may not be suitable for measuring ROM. This isotonic knee exercise monitor could detect and collect information on a patient's exercise activity for the benefit of healthcare providers.

Glucose exchange parameters in a subset of physiological conditions.

The chemical exchange of labile protons of the hydroxyl groups can be exploited in a variety of magnetic resonance experiments to gain information about the groups and their physicochemical environment. The exchangeable -OH protons provide important contributions to the T2 of water signals thus contributing to the T2-weighted contrast of MRI images. This exchange can be exploited more specifically and sensitively in chemical exchange saturation transfer (CEST) or longitudinal rotating frame relaxation (T1,ρ) experiments. Since glucose is omnipresent in living organisms, it may be seen as a rather universal probe. Even though the potential was first recognized many years ago, practical use has remained scarce due to numerous challenges. The major limitation is the rather low glucose concentration in most tissues. The other obstacles are related to multiple dependencies of the exchange parameters, such as temperature, pH, and concentration of various ions that are not known in sufficient detail for glucose. Thus, we embarked on evaluating the exchange parameters of a model that included every relevant chemical site for all -OH protons in both dominant enantiomers of glucose. We have (1) obtained conventional one-dimensional proton NMR spectra of glucose solutions in suitable temperature ranges, (2) we have iterated through several exchange models with various degrees of freedom determined by the number of distinguishable -OH proton sites and compared their performance, (3) we extrapolated the parameters of the best model of physiological temperature and (4) we demonstrated the use of the parameters in virtual experiments. As the main results, (1) we have obtained the temperature dependence of exchange parameters with reliable confidence intervals in three different pH values, with two of them reaching physiological temperature, and (2) we show how the parameters can be used in virtual experiments, helping to develop new applications for glucose as an NMR/MRI probe.

Association of Proliferative Diabetic Retinopathy in the Elderly with the Blood Complement System

A common complication of diabetes mellitus, mainly type 2, is diabetic retinopathy, among which the most unfavorable form for complete loss of vision is considered to be proliferative diabetic retinopathy. The participation of the complement system in the development of proliferative diabetic retinopathy is mainly devoted to experimental work on a limited number of blood complement components and without assessing their risk in the pathogenesis of the disease. The purpose of the study was to determine the association of components of the blood serum complement system with the development of proliferative diabetic retinopathy in the elderly. In clinical conditions, 115 patients 60–74 years old suffering from proliferative diabetic retinopathy and 48 patients of the same age with the absence of this ophthalmopathology were examined. The components of the blood complement system were studied by enzyme immunoassay and hemolytic method. The relative risk of the influence of the complement components was calculated according to the generally accepted method. There was a statistically significant increase in the blood serum of patients with proliferative diabetic retinopathy of most components of the complement system, with the exception of the C1 ing. and C5 components. The content of the C3a component increased especially to 127.6 ± 4.7 ng / ml versus 30.4 ± 3.5 ng/ml in the control, the C5a component to 5.6 ± 0.5 ng/ml versus 2.4 ± 0.3 ng/ml, and factor H to 228.7 ± 4.9 versus 106.3 ± 3.8 mng / ml, respectively. The highest value of the relative risk among the studied components is inherent in the C3a component of the blood complement with a reliable confidence interval of 4,451–5,103. The development of proliferative diabetic retinopathy in the elderly is associated with an increased content of C3a, C5a components and factor H in the blood serum, which can be used to develop targeted therapy for this disease.

Assessing critical point signatures through proton intermittency in NA61/SHINE

The search for experimental signatures of the critical point (CP) of strongly interacting matter is one of the main objectives of the NA61/SHINE experiment at CERN SPS. One such candidate observable is local fluctuations of the proton density in transverse space, constituting an order parameter of the chiral phase transition, and expected to scale according to a universal powerlaw in the vicinity of the CP. Its scaling can be probed through an intermittency analysis of the proton second scaled factorial moments (SSFMs) in transverse momentum space. The first such analysis [1] revealed power-law behavior in NA49 Si+Si collisions at 158A GeV/c, with a fitted exponent value consistent with the critical prediction, within errors. In the present work, we discuss known challenges posed by standard intermittency analysis in the face of low to moderate event statistics, and propose a novel technique that solves them. We perform a scan of Monte Carlo models simulating alternative critical and background scenarios, and weigh them against experimental results; we explore the method’s efficacy on simulated data. Once adapted to the available NA61/SHINE systems, the method will allow us to obtain reliable confidence intervals for the intermittency index (power-law ex-ponent) ϕ2 compatible with the experimental data.