Search Results (5)

Background: Electrochemical impedance spectroscopy (EIS) is indispensable for disentangling charge-transfer, capacitive, and diffusive phenomena, yet reproducible parameter estimation and objective model selection remain unsettled. Methods: We derive closed-form impedances and analytical Jacobians for seven equivalent-circuit models (Randles, constant-phase element (CPE), and Warburg impedance (ZW) variants), enforce physical bounds, and fit synthetic spectra with 2.5% and 5.0% Gaussian noise using hybrid optimization (Differential Evolution (DE) → Levenberg–Marquardt (LM)). Uncertainty is quantified via non-parametric bootstrap; parsimony is assessed with root-mean-square error (RMSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC); physical consistency is checked by Kramers–Kronig (KK) diagnostics. Results: Solution resistance ($R_s$) and charge-transfer resistance ($R_{ct}$) are consistently identifiable across noise levels. CPE parameters $(Q,n)$ and diffusion amplitude $\left(\sigma \right)$ exhibit expected collinearity unless the frequency window excites both processes. Randles suffices for ideal interfaces; Randles+CPE lowers AIC when non-ideality and/or higher noise dominate; adding Warburg reproduces the ${45}^{\circ }$ tail and improves likelihood when diffusion is present. The $(R_{ct}+Z_W)\Vert \mathrm{CPE}$ architecture offers the best trade-off when heterogeneity and diffusion coexist. Conclusions: The framework unifies analytical derivations, hybrid optimization, and rigorous statistics to deliver traceable, reproducible EIS analysis and clear applicability domains, reducing subjective model choice. All code, data, and settings are released to enable exact reproduction. Full article

Estimating confidence intervals in small or noisy datasets is a recurring challenge in biomolecular research, particularly when data contain outliers or exhibit high variability. This study introduces a robust statistical method that combines a hybrid bootstrap procedure with Steiner’s most frequent value (MFV) approach to estimate confidence intervals without removing outliers or altering the original dataset. The MFV technique identifies the most representative value while minimizing information loss, making it well suited for datasets with limited sample sizes or non-Gaussian distributions. To demonstrate the method’s robustness, we intentionally selected a dataset from outside the biomolecular domain: a fast-neutron activation cross-section of the ¹⁰⁹Ag(n, 2n)^108mAg reaction from nuclear physics. This dataset presents large uncertainties, inconsistencies, and known evaluation difficulties. Confidence intervals for the cross-section were determined using a method called the MFV–hybrid parametric bootstrapping (MFV-HPB) framework. In this approach, the original data points were repeatedly resampled, and new values were simulated based on their uncertainties before the MFV was calculated. Despite the dataset’s complexity, the method yielded a stable MFV estimate of 709 mb with a 68.27% confidence interval of [691, 744] mb, illustrating the method’s ability to provide interpretable results in challenging scenarios. Although the example is from nuclear science, the same statistical issues commonly arise in biomolecular fields, such as enzymatic kinetics, molecular assays, and diagnostic biomarker studies. The MFV-HPB framework provides a reliable and generalizable approach for extracting central estimates and confidence intervals in situations where data are difficult to collect, replicate, or interpret. Its resilience to outliers, independence from distributional assumptions, and compatibility with small-sample scenarios make it particularly valuable in molecular medicine, bioengineering, and biophysics. Full article

The Chalk River Laboratories (CRL) site in Ontario, Canada, has long been a hub for nuclear research, which has resulted in the accumulation of legacy nuclear waste, including radioactive materials such as uranium, plutonium, and other radionuclides. Effective management of this legacy requires precise contamination and risk assessments, with a particular focus on the concentration levels of fissile materials such as ${}^{235}\mathrm{U}$. These assessments are essential for maintaining nuclear criticality safety. This study estimates the upper bounds of ${}^{235}\mathrm{U}$ concentrations. We investigated the use of a hybrid parametric bootstrapping method and robust statistical techniques to analyze datasets with outliers, then compared these outcomes with those derived from nonparametric bootstrapping. This study underscores the significance of measuring ${}^{235}\mathrm{U}$ for ensuring safety, conducting environmental monitoring, and adhering to regulatory compliance requirements at nuclear legacy sites. We used publicly accessible ${}^{235}\mathrm{U}$ data from the Eastern Desert of Egypt to demonstrate the application of these statistical methods to small datasets, providing reliable upper limit estimates that are vital for remediation and decommissioning efforts. This method seeks to enhance the interpretation of sensor data, ultimately supporting safer nuclear waste management practices at legacy sites such as CRL. Full article

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion. Full article

Nowadays, the sustainability risks and opportunities start to affect strongly insurance companies in regard to the resulting additional variability of future values of variables taken into account in the decision processes. This is important especially in the era of sustainable non-life insurance promoting, among others, the use of ecological car engines or ecological systems of building heating. The fundamental issue in non-life insurance is to predict future claims (e.g., the aggregate value of claims or the number of claims for a single policy) in a heterogeneous portfolio of policies taking account of claim experience. For this purpose, the so-called credibility theory is used, which was initiated by the fundamental Bühlmann model modified to the Bühlmann–Straub model. Several modifications of the model have been proposed in the literature. One of them is the development of the relationship between the credibility models and statistical mixed models (e.g., linear mixed models) for longitudinal data. The article proposes the use of the parametric bootstrap algorithm to estimate measures of accuracy of the credibility predictor of the number of claims for a single policy taking into account new risk factors resulting from the emergence of green technologies on the considered market. The predictor is obtained for the model which belongs to the class of Generalised Linear Mixed Models (GLMMs) and which is a generalization of the Bülmann–Straub model. Additionally, the possibility of predicting the number of claims and the problem of the assessment of the prediction accuracy are presented based on a policy characterized by new green risk factor (hybrid motorcycle engine) not previously present in the portfolio. The paper presents the proposed methodology in a case study using real insurance data from the Polish market. Full article