Interval Estimation Method Research Articles

Analysis and applications of Nakagami constant-stress model using progressive Type-II censored data

Abstract In the case of trustworthy products, accelerated life tests are crucial techniques used to gather information regarding the lifetime of the target population with a shorter time frame compared to routine investigations. The received data in higher stress levels than normal are then used to predict the reliability of the product under consideration in regular working circumstances. In this paper, the constant-stress accelerated life tests are employed when the data are obtained through a progressive Type-II censoring strategy from Nakagami populations. Besides estimating the model parameters, the reliability function under the usual use conditions is predicted using four estimation procedures. The maximum likelihood, least squares, weighted least squares and maximum product of spacing estimation approaches are utilized for estimation purposes. In addition, two interval estimation methods are considered utilizing the asymptotic features of the maximum likelihood and maximum product of spacing estimates. A simulation investigation is conducted to evaluate the efficiency of diverse point and interval estimations beneath various strategies involving sample sizes, effective number of failures, and removal designs. From a practical perspective, a pair of datasets related to the failure times of coupons cut from aluminum sheeting and white organic light-emitting diodes are explored to confirm the effectiveness of the theoretical findings.

Accelerated Degradation Data Analysis Based on Gamma Process With Random Effects

ABSTRACTThe Gamma constant‐stress accelerated degradation model is a natural model for monotonous degradation processes. However, unit heterogeneity often exists in practice, necessitating a more realistic model. This study develops a Gamma process with random effects to accurately capture accelerated degradation data for reliability analysis, encompassing both point and interval estimation. First, the Expectation‐Maximization (EM) algorithm is developed to obtain point estimates of the proposed model. Since these estimates are sensitive to initial values, potentially impacting the outcomes, an improved EM algorithm is proposed, which iteratively refines the estimation quality by executing two different M‐steps, thereby enhancing overall estimation accuracy. Secondly, given the complexity of the model and the constraint of small sample sizes and limited stress levels, a three‐step interval estimation method is devised. This method segregates the parameters into three distinct parts and addresses them individually using the generalized pivotal quantity method, which simplifies the parameter interval estimation process and enhances the estimation accuracy. Finally, simulation studies and a real example of O‐rings are presented to demonstrate the effectiveness of the proposed method.

Interval estimation for Topp-Leone distribution

. This article presents several point estimation and interval estimation methods for the Topp-Leone distribution and applies them to the stress-strength model. A new moment estimation and inverse estimation are derived. The algorithm of the maximum likelihood estimation is discussed. Using the generalized pivotal quantity method, the generalized confidence intervals for model parameters and some reliability metrics are also obtained. For the estimation on reliability of stress-strength model, the generalized confidence intervals and bootstrap-p confidence intervals are given. The performance of the proposed methods is assessed by Monte Carlo simulation. Finally, a real example is used to illustrate the proposed methods.

Comparative soil bacterial metabarcoding after aboveground vs. subsurface decomposition of Mus musculus

Outdoor microcosms, metabarcoding with next-generation sequencing of the 16S rRNA bacterial gene, total body score (TBS) and physicochemical analyses were used to monitor Mus musculus decomposition aboveground (A) and in the subsurface (S), and compared to soil-only controls (C). As determined by MaAsLin2 analysis, significant shifts in bacterial communities at 30 cm depths within the A, S and C treatments distinguished control from experimental soils, and between aboveground and subsurface deposition, demonstrating the potential for gravesoil discrimination during the first 90 days. For example, Dokdonella (p = 0.0002), Edaphobaculum (p = 0.0004) and Lacibacter (p = 0.0034) recorded significant shifts relative to sampling time. Furthermore, Massilia (p = 0.0005), Mycobacterium (p = 0.0006) and Sandaracinus (p = 0.0007) increased in abundance for the aboveground mice treatments. This was confirmed with ANOSIM where p = 0.0082 showed statistically significant difference between the aboveground and subsurface deposition. TBS and physicochemical analyses suggested that nutrient release into the soils occurred during active decay and skin rapture on days 7–13 in the subsurface and days 13–20 aboveground, with a particular increase in soil potassium concentration on day 15. Significant differences in soil temperatures resulted between A and S vs. C microcosms, aligning with atmospheric temperature changes. In summary, complementary application of metabarcoding, total body score, exogenous and physicochemical methods for postmortem interval estimation and clandestine grave location highlighted the feasibility of using temperature records downloaded from meteorological stations and portable X-ray fluorescence as indicators for various phases of decomposition.

Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution

In this paper, we propose statistical inference methodologies for estimating the shape parameter α of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for α and (2) a fixed-accuracy confidence interval estimation method for α. For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures.

Finite‐Time Functional Interval Observer Design for Nonlinear Discrete‐Time Switched Descriptor Systems

ABSTRACTIn this article, the finite‐time functional interval estimation method for nonlinear discrete‐time switched descriptor systems with perturbations is investigated. To deal with the nonlinear terms in the switched system, the nonlinear error system is converted into a linear parameter varying form using the reformulated Lipschitz property. Firstly, a functional observer with finite‐time gain is constructed for the nonlinear switched descriptor system. Then, based on the proposed finite‐time functional observer, the reachability analysis is applied to design a finite‐time functional interval observer. Finally, the superiority and effectiveness of the interval estimation method presented in this paper are verified through a simulation of the circuit system.

Interval state estimation method for distribution networks considering multi-attribute decision making and multi-source measurement data uncertainty

The operation of distribution networks faces significant challenges due to uncertainties and measurement errors. This paper presents an innovative interval state estimation method that leverages multisource measurement data and multi-attribute decision-making to enhance accuracy and reliability. We first extract deterministic uncertainty measures from heterogeneous measurement data. By analyzing the interplay between determinacy and uncertainty, we construct an interval representation space that enables precise extraction, integration, and analysis of multisource data. Subsequently, we develop an interval multi-attribute decision-making model that reflects the dynamic preferences of the distribution network, resulting in a robust interval state estimation model that incorporates uncertainty. An improved Krawczyk-Moore (KM) algorithm facilitates iterative solutions, while Monte Carlo simulations validate the model's effectiveness in handling multisource data fusion and uncertainty analysis. Simulation results demonstrate a 0.02 improvement in measurement error statistics, with estimation error statistics remaining stable and the estimated interval coverage probability decreasing by approximately 0.4. Overall, this method outperforms traditional approaches, particularly in scenarios characterized by data uncertainty and multisource data integration, thereby enhancing estimation accuracy.

Reliability analysis of load sharing systems under unequal load-sharing rule with applications

We are examining a setup consisting of several parallel-connected k-out-of-m load sharing systems. The load sharing is modeled using proportional conditional failure rates for component failures and load sharing under the unequal load-sharing rule. We have derived the system reliability for the entire setup. To illustrate this, we examine two cases: one with n systems connected in parallel, each following a 1-out-of-2 configuration, and the other with n systems connected in parallel, each following a 2-out-of-4 configuration. The system components are assumed to be identical with an exponential as well as Weibull baseline distributions. We propose two methods to estimate the baseline parameter and load-sharing parameters. Additionally, we present a confidence interval using bootstrapping techniques, specifically the percentile bootstrap (boot-p). We assess the performance of these parameter estimation and interval estimation methods through simulation studies. Furthermore, we evaluate the practical applicability of the proposed techniques by analyzing two real datasets. The same approach can be applied to a system that includes multiple k-out-of-m load sharing systems, where these systems are connected in either a series or a p-out-of-q configuration.

Environmental predictors impact microbial-based postmortem interval (PMI) estimation models within human decomposition soils.

Microbial succession has been suggested to supplement established postmortem interval (PMI) estimation methods for human remains. Due to limitations of entomological and morphological PMI methods, microbes are an intriguing target for forensic applications as they are present at all stages of decomposition. Previous machine learning models from soil necrobiome data have produced PMI error rates from two and a half to six days; however, these models are built solely on amplicon sequencing of biomarkers (e.g., 16S, 18S rRNA genes) and do not consider environmental factors that influence the presence and abundance of microbial decomposers. This study builds upon current research by evaluating the inclusion of environmental data on microbial-based PMI estimates from decomposition soil samples. Random forest regression models were built to predict PMI using relative taxon abundances obtained from different biological markers (bacterial 16S, fungal ITS, 16S-ITS combined) and taxonomic levels (phylum, class, order, OTU), both with and without environmental predictors (ambient temperature, soil pH, soil conductivity, and enzyme activities) from 19 deceased human individuals that decomposed on the soil surface (Tennessee, USA). Model performance was evaluated by calculating the mean absolute error (MAE). MAE ranged from 804 to 997 accumulated degree hours (ADH) across all models. 16S models outperformed ITS models (p = 0.006), while combining 16S and ITS did not improve upon 16S models alone (p = 0.47). Inclusion of environmental data in PMI prediction models had varied effects on MAE depending on the biological marker and taxonomic level conserved. Specifically, inclusion of the measured environmental features reduced MAE for all ITS models, but improved 16S models at higher taxonomic levels (phylum and class). Overall, we demonstrated some level of predictability in soil microbial succession during human decomposition, however error rates were high when considering a moderate population of donors.

A hybrid BWM–CRITIC–VIKOR approach for assessing oil and gas risk scenarios in probabilistic linguistic term set

The oil and gas industry plays a crucial role in supporting energy supply and economic development. Mitigating risks in oil and gas projects is essential for reducing decision-making uncertainties, optimizing resource allocation, and fostering the competitiveness and sustainable growth of enterprises. Therefore, evaluating decision-making risks in the oil and gas sector is of significant practical importance. This paper proposes a comprehensive approach based on the BWM–CRITIC–VIKOR multi-criteria decision-making (MCDM) evaluation model. An evaluation index system encompassing six critical dimensions—technology, economics, environment, security, societal impact, and political factors—is established. To enhance assessment precision, the AHP interval estimation method is employed to identify and eliminate indicators with low contributions. Subsequently, the probabilistic linguistic term set (PLTS) is introduced into the best–worst method (BWM) and CRITIC methods to calculate the weights for each index. This approach helps to circumvent the subjectivity inherent in single subjective weighting methods. To evaluate and rank alternatives, the PLTS is used as an evaluation linguistic tool within the VIKOR framework. Finally, this methodology is applied to decision-making in the oil and gas industry, and its effectiveness and superiority are compared with the AHP–TOPSIS method and the BWM–CRITIC method.

β values obtained by linear regression models of morpho-physiological and biochemical variables as novel drought stress estimators in Capsicum annuum varieties

Capsicum annuum varieties are highly sensitive to drought. Under water stress conditions, these can show yield losses of up to 70 %. Due to the above, this work proposes a novel approach to obtain estimators of drought stress based on linear regression models for morpho-physiological and biochemical variables in jalapeño pepper (C. annuum cv. jalapeno M), bell pepper (C. annuum cv. california wonder), and serrano pepper (C. annnuum cv. serrano tampiqueno). Jalapeno pepper plants were grown for 69 days under permanent water deficit conditions at 40, 60, 80 % and 100 % of field capacity (FC) (100 % FC as control). Throughout the crop cycle, we monitored the plant's height and weight, basal stem diameter, transpiration, photosynthesis, stomatal conductance, NDVI, and proline. This monitoring allowed us to obtain linear regression models from the accumulated values for these variables, from which the slope values (β) were used as estimators of drought stress using the interval estimation method, in the same way, this method was used to estimate water status in bell pepper and serrano pepper. For bell pepper, drought levels of 40, 60, 80 and 100 % FC were imposed for 12 days and serrano pepper 60 and 100 % FC for 63 days. The results showed that this method can be used to estimate drought stress in jalapeno pepper for all the irrigation levels through photosynthesis and NDVI and can be applied for bell pepper and serrano pepper using stem diameter and plant height, and in the case of serrano pepper, NDVI showed adequate results. Also, this work establishes the relationship between the jalapeno pepper responses (morpho-physiological and biochemical) to drought stress during vegetative, flowering, and fruiting stages through a Principal Component Analysis (PCA). The PCA found that interaction among morphological, physiological, and biochemical responses change concerning the phenological stage of the plant. The results suggested several direct and inverse relationships between the variables and showed that drought can be described by stomatal conductance during any phenological stage of the crop. In parallel, the proline content, NDVI and plant height can also describe drought stress during the vegetative and flowering stages. This research is the first to apply this methodology to drought stress estimation in jalapeno, bell pepper, and serrano pepper cultivation. The results could significantly contribute to precision agriculture, sensor development, and water management.

Simultaneous interval estimation of actuator fault and state for a class of nonlinear systems by zonotope analysis

In this paper, an actuator fault and state interval estimation method for a class of nonlinear systems is proposed by integrating observer design and zonotope analysis. For the considered systems, we present a novel unknown input observer structure with broad applications. The design procedure is based on H∞ method to decrease the influence of unknown but bounded process disturbances and measurement noise. Moreover, a novel interval estimation method is presented based on zonotope analysis to obtain tighter intervals. Numerical simulations of a quadruple-tank system are conducted to assess the performance of the proposed approach.

Indirect reference interval estimation using a convolutional neural network with application to cancer antigen 125

Indirect methods for reference interval (RI) estimation, which use data acquired from routine pathology testing, have the potential to accelerate the establishment of RIs to account for variables such as gender and age to improve clinical assessments. However, they require more sophisticated methods of analysis due to the potential influence of pathological patients in raw clinical datasets. In this paper we develop a novel convolutional neural network (CNN) model trained on synthetic data to identify underlying healthy distributions within pathological admixtures. We present both the methodology to generate synthetic data and the CNN model. We evaluate the CNN using two synthetic test datasets, including samples from a proposed benchmark for indirect methods (RIBench) and show significant improvements compared to the reported state-of-the-art method based on the benchmark (refineR). We also demonstrate a real-world application of the model, estimating age-specific RIs for cancer antigen 125 (CA-125), a crucial biomarker for ovarian cancer diagnostics. Our results show that CA-125 RIs are strongly age-dependent, which could have important diagnostic consequences.

How Gaussian mixture modelling can help to verify reference intervals from laboratory data with a high proportion of pathological values

Abstract Objectives Although there are several indirect methods that can be used to verify reference limits, they have a common weakness in that they assume a low proportion of pathological values. This paper investigates whether a Gaussian decomposition algorithm can identify the non-pathological fraction even if it is not the main subset of mixed data. Methods All investigations are carried out in the R programming environment. The mclust package is used for Gaussian mixture modelling via the expectation maximization (EM) algorithm. For right-skewed distributions, logarithms of the original values are taken to approximate the Gaussian model. We use the Bayesian information criterion (BIC) for evaluation of the results. The reflimR and refineR packages serve as comparison procedures. Results We generate synthetic data mixtures with known normal distributions to demonstrate the feasibility and reliability of our approach. Application of the algorithm to real data from a Nigerian and a German population produces results, which help to interpret reference intervals of reflimR and refineR that are obviously too wide. In the first example, the mclust analysis of hemoglobin in Nigerian women supports the medical hypothesis that an anemia rate of more than 50 % leads to falsely low reference limits. Our algorithm proposes various scenarios based on the BIC values, one of which suggests reference limits that are close to published data for Nigeria but significantly lower than those established for the Caucasian population. In the second example, the standard statistical analysis of creatine kinase in German patients with predominantly cardiac diseases yields a reference interval that is clearly too wide. With mclust we identify overlapping fractions that explain this false result. Conclusions Gaussian mixture modelling does not replace standard methods for reference interval estimation but is a valuable adjunct when these methods produce discrepant or implausible results.

A multivariate student-t process model for dependent tail-weighted degradation data

Traditionally, the Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allowing the adjustment of tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation–maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.

Dental DNA Mutations Occurring after Death: A Novel Method for Post-Mortem Interval (PMI) Estimation.

Post-mortem interval (PMI) estimation remains one of the major challenges in forensic practice, especially for late PMIs beyond 7-10 days after the death of the subject. In 2022, an innovative method to investigate the occurrence of mutations induced by the death of a subject in the DNA of post-mortem dental pulps at different PMIs was developed, applying a next-generation sequencing (NGS) analysis. The present study aims to apply the same method of analysis to a small sample of teeth belonging to the same subject and analyzed at different PMIs/accumulated degree days (ADDs), and of teeth extracted from different subjects but analyzed at the same PMI/ADD to verify the repeatability of the results obtained in relation to the time elapsed since death. A total of 10 teeth were collected from 6 patients (3 males and 3 females) with PMI varying from 8 to 35 days, and ADD from 157.4 to 753.8. We found 1754 mutations in 56 genes, with more than 700 mutations having a prevalence > 5% and more than 300 variants considered of interest for the purposes of the study. Mutations that were not present at lower PMIs but manifested in later PMIs in pulps belonging to the same subject demonstrate that they can only have been acquired by the subject after death and according to the time elapsed since death. In total, 67 somatic mutations in 29 out of the 56 genes of the used panel occurred in a fashion that allows an association with specific PMI/ADD ranges (within 8 days, between 17 and 28, and beyond 30 days after death). The results suggest that temperature and humidity could influence the rate of DNA degeneration in dental pulps, thus PMI should be estimated in ADD more than days. The preliminary validation supports the hypothesis that the innovative method could be a useful tool for estimating the post-mortem interval even beyond the first week after death, but further analyses are needed to customize a specific genetic panel for forensic investigations and verify the influence of degenerative processes of soft tissues surrounding dental elements on DNA degeneration of pulps.

Optimal Cut-Point Selection Methods Under Binary Classification When Subclasses Are Involved.

In practice, we often encounter binary classification problems where both main classes consist of multiple subclasses. For example, in an ovarian cancer study where biomarkers were evaluated for their accuracy of distinguishing noncancer cases from cancer cases, the noncancer class consists of healthy subjects and benign cases, while the cancer class consists of subjects at both early and late stages. This article aims to provide a large number of optimal cut-point selection methods for such setting. Furthermore, we also study confidence interval estimation of the optimal cut-points. Simulation studies are carried out to explore the performance of the proposed cut-point selection methods as well as confidence interval estimation methods. A real ovarian cancer data set is analyzed using the proposed methods.

Doubly Robust Augmented Model Accuracy Transfer Inference with High Dimensional Features

Transfer learning is crucial for training models that generalize to unlabeled target populations using labeled source data, especially in real-world studies where label scarcity and covariate shift are common. While most research focuses on model estimation, there is limited literature on transfer inference for model accuracy despite its importance. We introduce a novel Doubly Robust Augmented Model Accuracy Transfer Inferen Ce (DRAMATIC) method for point and interval estimation of commonly used classification performance measures in an unlabeled target population with labeled source data. DRAMATIC derives and evaluates a potentially misspecified risk model for a binary response, leveraging high-dimensional adjustment features from both source and target data. It builds on an imputation model for the response mean and a density ratio model to characterize distributional shifts. The method constructs doubly robust estimators that are valid when either model is correctly specified and certain sparsity assumptions hold. Simulations show negligible bias in point estimation and satisfactory empirical coverage levels in confidence intervals. The utility of DRAMATIC is illustrated by transferring a genetic risk prediction model and its accuracy evaluation for type II diabetes across two patient cohorts in Mass General Brigham (MGB). Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

A comparison of Bayesian and score methods for interval estimates of positive/negative likelihood ratios in support of diagnostic device performance evaluation

ABSTRACT Background Positive and negative likelihood ratios (PLR and NLR) are important metrics of accuracy for diagnostic devices with a binary output. However, the properties of Bayesian and frequentist interval estimators of PLR/NLR have not been extensively studied and compared. In this study, we explore the potential use of the Bayesian method for interval estimation of PLR/NLR, and, more broadly, for interval estimation of the ratio of two independent proportions. Methods We develop a Bayesian-based approach for interval estimation of PLR/NLR for use as a part of a diagnostic device performance evaluation. Our approach is applicable to a broader setting for interval estimation of any ratio of two independent proportions. We compare score and Bayesian interval estimators for the ratio of two proportions in terms of the coverage probability (CP) and expected interval width (EW) via extensive experiments and applications to two case studies. A supplementary experiment was also conducted to assess the performance of the proposed exact Bayesian method under different priors. Results Our experimental results show that the overall mean CP for Bayesian interval estimation is consistent with that for the score method (0.950 vs. 0.952), and the overall mean EW for Bayesian is shorter than that for score method (15.929 vs. 19.724). Application to two case studies showed that the intervals estimated using the Bayesian and frequentist approaches are very similar. Discussion Our numerical results indicate that the proposed Bayesian approach has a comparable CP performance with the score method while yielding higher precision (i.e. a shorter EW).

A membership function-dependent L∞ performance based output interval estimation method for discrete-time Takagi–Sugeno fuzzy systems applied to fault detection

In the design process of traditional L∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L∞ performance index is proposed. The proposed L∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well.