Interval Estimation Research Articles

Minimum sample size for estimating the Net Promoter Score under a Bayesian approach.

At some moment in our lives, we are probably faced with the following question: How likely is it that you would recommend [company X] to a friend or colleague?. This question is related to the Net Promoter Score (NPS), a simple measure used by several companies as indicator of customer loyalty. Even though it is a well-known measure in the business world, studies that address the statistical properties or the sample size determination problem related to this measure are still scarce. We adopt a Bayesian approach to provide point and interval estimators for the NPS and discuss the determination of the sample size. Computational tools were implemented to use this methodology in practice. An illustrative example with data from financial services is also presented.

Meta-analysis of Censored Adverse Events

Meta-analysis is a powerful tool for assessing drug safety by combining treatment-related toxicological findings across multiple studies, as clinical trials are typically underpowered for detecting adverse drug effects. However, incomplete reporting of adverse events (AEs) in published clinical studies is frequently encountered, especially if the observed number of AEs is below a pre-specified study-dependent threshold. Ignoring the censored AE information, often found in lower frequency, can significantly bias the estimated incidence rate of AEs. Despite its importance, this prevalent issue in meta-analysis has received little statistical or analytic attention in the literature. To address this challenge, we propose a Bayesian approach to accommodating the censored and possibly rare AEs for meta-analysis of safety data. Through simulation studies, we demonstrate that the proposed method can improve accuracy in point and interval estimation of incidence probabilities, particularly in the presence of censored data. Overall, the proposed method provides a practical solution that can facilitate better-informed decisions regarding drug safety.

Analysis of Weibull progressively first-failure censored data with beta-binomial removals

<p>This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as beta-binomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies.</p>

Effects of Cold-Storage Temperature on the Accuracy of Death Interval Estimation Using the Thanatochemical Dynamics of Vitreous Humour and Synovial Fluid

Effects of Cold-Storage Temperature on the Accuracy of Death Interval Estimation Using the Thanatochemical Dynamics of Vitreous Humour and Synovial Fluid

Inference for a general family of exponentiated distributions under ranked set sampling with partially observed complementary competing risks data

ABSTRACT Ranked set sampling (RSS) acts as an efficient way for collecting failure information due to its ability of saving testing time and cost, and this paper discusses statistical inference for complementary competing risks model under a modified RSS scheme called the maximum ranked set sampling procedure with unequal samples (MRSSU). When the lifetimes of causes of failure are characterized by a general family of exponentiated distributions with partially observed failure causes, parameter estimation is explored from classical likelihood and Bayesian approaches. Existence and uniqueness of maximum likelihood estimators for model parameters are established, and approximate confidence intervals are constructed in consequence. With respect to general flexible priors, Bayes point and interval estimates are constructed, and associated Monte-Carlo sampling is proposed for complex posterior computation. In addition, when there is extra restriction information available, likelihood and Bayes estimates are also proposed in this regard. Extensive simulation studies are conducted to investigate the performance of different methods, and a real-life example is carried out to demonstrate the applications of our results.

Short-term Detection of Fast Progressors in Glaucoma: The Fast Progression Assessment through Clustered Evaluation (Fast-PACE) Study

To evaluate the performance of an intensive, clustered testing approach in identifying eyes with rapid glaucoma progression over 6 months in the Fast-PACE (Progression Assessment through Clustered Evaluation) study. Prospective cohort study. 125 eyes from 65 primary open-angle glaucoma (POAG) subjects. Subjects underwent two sets of 5 weekly visits (clusters) separated by an average of 6 months, then were followed with single visits every 6 months for an overall mean follow-up of 25 months (mean of 17 tests). Each visit consisted of testing with standard automated perimetry (SAP) 24-2 and 10-2, and spectral-domain optical coherence tomography (SD OCT). Progression was assessed using trend analyses of SAP mean deviation (MD) and retinal nerve fiber layer (RNFL) thickness. Generalized estimating equations were applied to adjust for correlations between eyes for confidence interval (CI) estimation and hypothesis testing. Diagnostic accuracy of the 6-month clustering period to identify progression detected during the overall follow-up. 19 of 125 eyes (15%, CI: 9%-24%) progressed based on SAP 24-2 MD over the 6-month clustering period. 14 eyes (11%, CI: 6%-20%) progressed on SAP 10-2 MD, and 16 (13%, CI:8%-21%) by RNFL thickness, with 30 of 125 eyes (24%, CI:16%-34%) progressing by function, structure, or both. Of the 35 eyes progressing during the overall follow-up, 25 had progressed during the 6-month clustering period, for a sensitivity of 71% (CI: 53%-85%). Of the 90 eyes that did not progress during the overall follow-up, 85 also did not progress during the 6-month period, for a specificity of 94% (CI: 88% - 98%). Of the 14 eyes considered fast progressors by SAP 24-2, 10-2 or SD OCT during the overall follow-up, 13 were identified as progressing during the 6-month cluster period, for a sensitivity of 93% (CI: 66% - 100%) for identifying fast progression with a specificity of 85% (CI: 77% - 90%). Clustered testing in the Fast-PACE study detected fast-progressing glaucoma eyes over six months. The methodology could be applied in clinical trials investigating interventions to slow glaucoma progression and may also be of value for short-term assessment of high-risk subjects.

An Interval Observer for a Class of Cyber–Physical Systems with Disturbance

This paper investigates the problem of interval estimation for cyber–physical systems with unknown disturbance. In order to realize the interval estimation of cyber–physical systems, two technical methods are adopted. The first one requires the observer dynamic error system to be non-negative, and the second one relaxes this limitation by coordinate transformation. The sufficient conditions are established using both Lyapunov stability and positive system theory. Furthermore, according to the Schur complement, the linear matrix inequality is solved to determine the observer gains. Finally, the effectiveness and feasibility of the designed interval observer are verified by one numerical simulation.

Uncertain quantile autoregressive model

The propose of uncertain time series is to explore the relationship between response variables and explanatory variables over time based on the imprecise observations. In order to more comprehensively describe the overall picture of the relationship between variables under the time series, a new uncertain quantile autoregressive model is proposed. By studying the uncertain quantile autoregressive model, the estimated method under different quantiles of its unknown parameters is proposed. Based on the fitted uncertain quantile autoregressive model, the residual is analyzed. Furthermore, uncertainty hypothesis testing are used to verify the reasonableness and accuracy of the estimates under different quantiles. Moreover, the point estimate and interval estimate of the predicted value are presented. Finally, the rationality and validity of the model are verified by two examples.

Interval Estimation of the Stress-Strength Reliability in Lehmann Family of Distributions

This paper presents a unified approach for computing confidence limits for stress–strength reliability when strength and stress are independent random variables following a distribution in Lehmann family. The generalized confidence interval and the bootstrap confidence intervals are obtained. Simulation studies are conducted to assess the performance of the proposed methods in terms of the estimated coverage probabilities and the length of the confidence intervals. An example is also provided for illustration.

An integrated Bayesian framework for multi-omics prediction and classification.

With the growing commonality of multi-omics datasets, there is now increasing evidence that integrated omics profiles lead to more efficient discovery of clinically actionable biomarkers that enable better disease outcome prediction and patient stratification. Several methods exist to perform host phenotype prediction from cross-sectional, single-omics data modalities but decentralized frameworks that jointly analyze multiple time-dependent omics data to highlight the integrative and dynamic impact of repeatedly measured biomarkers are currently limited. In this article, we propose a novel Bayesian ensemble method to consolidate prediction by combining information across several longitudinal and cross-sectional omics data layers. Unlike existing frequentist paradigms, our approach enables uncertainty quantification in prediction as well as interval estimation for a variety of quantities of interest based on posterior summaries. We apply our method to four published multi-omics datasets and demonstrate that it recapitulates known biology in addition to providing novel insights while also outperforming existing methods in estimation, prediction, and uncertainty quantification. Our open-source software is publicly available at https://github.com/himelmallick/IntegratedLearner.

The Diversity of Forensic Entomofauna Associated With Decaying Chicken Liver in the Tropical Region of Kerala, India.

Forensic entomology To elucidate the time of death based on insect evidence, there are several studies on forensic entomology on life cycles, environmental factors, and feeding habitats of insects. However, there have not been any comprehensive studies on forensic entomology and its usage in forensic inquiry specific to the region, especially Kerala, India. The insect succession on decomposed animal matter plays an important role in estimating minimum postmortem intervals (mPMI). Objective The purpose of the study was tounderstand forensically important insect groups and their role in the decomposition process of dead decayingmatter. The different decomposition stages of a corpse vary in attraction to necrophagous insects and the insect fauna depending on its prevailing conditions of decay. The decomposition is highly dependent on the exposition of animal matter and abiotic and biotic factors acting on it. The main objective of the present investigation was to identify the insect fauna associated with decaying chicken liver. The study also envisages comprising the diversity and abundance of insects between two different treatments of animal matter: in contact with soil and controlled conditions in a clean basin. Method The study was conducted for 45 days (until the total decomposition of the samples in both conditions) during the pre-monsoon months of April to May2022 at Chalikadavu, Muvattupuzha, in the Ernakulam district, Kerala, India. The samples were however kept away from direct sunlight and rain to avoid the direct impact on the orienting fauna. The entomofauna found to be associated with the decaying animal matter was carefully collected from the site and stored in 70% isopropyl alcohol for preservation. The total number of insects was recorded along with the hours of maximum incidence, and samples were stored in plastic vials for further identification. Result In this study, we analyzed the activities of ants, mites, wasps, cockroaches, moths, beetles, and flies during the decomposition of decaying chicken liver. Among these insects, flies and beetles are two important arthropod communities associated with animal matter decomposition. We collected these foraging organisms for morpho-taxonomic identification. The decomposition stages among the two treatments could help to understand the variable factors in the decomposition of decaying corpse with special reference to the insect fauna acting on it. Conclusion We got 100 specimens comprising 28 species in 17 families from Blattidae, Coleoptera, Diptera, Hymenoptera, and Lepidoptera. Besides this, we identified two parasitic wasps with their host (dipteran pupa), which is helpful in postmortem interval (PMI) estimation. Our analysis showed an association between decay and the activity of carrion insects. The decomposition stages among the two treatments could help to understand the variable factors in the decomposition of a decaying corpse with special reference to the insect fauna acting upon it.

Post-averaging inference for optimal model averaging estimator in generalized linear models

This article considers the problem of post-averaging inference for optimal model averaging estimators in a generalized linear model (GLM). We establish the asymptotic distributions of optimal model averaging estimators for GLMs. The asymptotic distributions of the model averaging estimators are nonstandard, depending on the configuration of the penalty term in the weight choice criterion. We also propose a feasible simulation-based confidence interval estimator and investigate its asymptotic properties rigorously. Monte Carlo simulations verify the usefulness of our theoretical results, and the proposed methods are employed to analyze a stock car racing dataset.

High-frequency data significantly enhances the prediction ability of point and interval estimation

Accurate prediction of dissolved oxygen (DO) dynamics is crucial for understanding the influence of environmental factors on the stability of aquatic ecosystem. However, limited research has been conducted to determine the optimal frequency of water quality monitoring that ensures continuous assessment of water health while minimizing costs. To address these challenges, the present study developed a hybrid stochastic hydrological model (i.e., ARIMA-GARCH hybrid model) and machine learning (ML) models. The objective of this study is to identify the best-performing model and establish the optimal monitoring frequency. Results revealed that high-frequency DO monitoring data exhibit greater variability compared to low-frequency data. Moreover, the ARIMA-GARCH model demonstrates promising potential in predicting DO concentrations for low-frequency monitoring data, surpassing ML models in performance. Furthermore, increasing the monitoring frequency significantly improves the prediction accuracy of models, regardless of whether point (with lower R2 values of 0.64 and 0.51 for daily detection than these of every 15 min (0.96 and 0.99) at CHQ and LHT, respectively) or interval predictions (with RIW higher values of 2.00 and 1.55 for daily detection higher than these of 0.02 and 0.16 in every 15 min at CHQ and LHT, respectively) are considered. Additionally, a 4 hourly monitoring frequency was found to be optimal for water quality assessment using each model. These findings identify the superior performing of the ARIMA-GARCH model and highlight the crucial role of monitoring frequency in enhancing DO prediction and improving model performance.

Distorted correlations among censored data: causes, effects, and correction.

Data censoring occurs when researchers do not know precise values of data points (e.g., age is 55+ or concentration ≤ .001). Censoring is frequent within psychology but typically unrecognized outside of longitudinal studies. We describe five circumstances when censoring may occur, demonstrate censoring distorts correlations, and discuss how censoring can create spurious factors. Next, we explain how to use R package lava to calculate maximum likelihood estimates (Holst and Budtz-JørgensenComputational Statistics, 28(4), 1385-1452,2013) of correlations between uncensored variables based upon censored variables. Previous research demonstrated these estimates were more accurate than Muthén's (1984) estimate for one particular model, but no research has systematically examined their accuracy. We therefore conducted a simulation study exploring the effects of the correlation, sample size, and censoring on point and interval estimates of correlations. Based upon 80 cells in which low values of normally distributed variables were censored, we recommend the constrained regression model with Wald confidence intervals. These methods were precise and unbiased unless both variables had 70% censoring and the correlation was large and negative (e.g., -.9), in which case estimates were closer to -1 than they should be. Opposite results would occur if low values of one variable and high values of the other were censored: Estimates would be precise and unbiased unless censoring was extreme and correlations were large and positive. To estimate large correlations accurately, we recommend researchers reduce censoring by using longer longitudinal studies, using scales with more response options, and matching measures to populations to reduce floor and ceiling effects.

Reactor reliability modeling and reliable life analysis method for multi-state space reactor systems based on DBN and interval estimation

Space nuclear reactor power (space reactor) is of the highest energy density and the most promising long-term self-sustaining and high-power level space power source. Achieving high reliability during the years-long maintenance-free service process is one of the bottlenecks that constrain the application of space reactors, which brings a challenging task on the quantitative evaluation of reliability indicators (life and reliability) of space reactors during the design phase. On the one hand, traditional binary reliability theory cannot model the system functional structure accurately, due to diverse failure modes and complex propagation paths; on the other hand, the lack of reliability data introduces large epistemic uncertainty, resulting from high costs and time-consuming ground reliability tests. To tackle these problems, this paper takes the Stirling integrated space reactor (ACMIR) as a specific research object and proposes a general reactor reliability modeling and reliable life analysis method for space reactors with large prior epistemic uncertainty which is robust to manipulation and can obtain system reliability indicators with small confidence intervals for engineering decisions. First, based on experts’ experience, the functional logic relationship between components and system is sorted out by the failure mode and effect analysis (FMEA) and the prior failure rates of components are evaluated according to the failure grade of the industrial standard. Then, the FMEA model is mapped to a discrete-time Bayesian network (DBN) to model the system reliable life, based on which system reliability indicators with low epistemic uncertainty are analyzed by interval estimation. Finally, the practical and engineering value of the proposed method is demonstrated with the example of ACMIR in two application cases.

Development of a deviation package method for low-cost robust optimization in compressor blade design

Manufacture variations can greatly increase the performance variability of compressor blades. Current robust design optimization methods have a critical role in reducing the adverse impact of the variations, but can be affected by errors if the assumptions of the deviation models and distribution parameters are inaccurate. A new approach for robust design optimization without the employment of the deviation models is proposed. The deviation package method and the interval estimation method are exploited in this new approach. Simultaneously, a stratified strategy is used to reduce the computational cost and assure the optimization accuracy. The test case employed for this study is a typical transonic compressor blade profile, which resembles most of the manufacture features of modern compressor blades. A set of 96 newly manufactured blades was measured using a coordinate measurement machine to obtain the manufacture variations and produce a deviation package. The optimization results show that the scatter of the aerodynamic performance for the optimal robust design is 20% less than the baseline value. By comparing the optimization results obtained from the deviation package method with those obtained from widely-used methods employing the deviation model, the efficiency and accuracy of the deviation package method are demonstrated. Finally, the physical mechanisms that control the robustness of different designs were further investigated, and some statistical laws of robust design were extracted.

Indirect estimation of pediatric reference interval via density graph deep embedded clustering

Establishing reference intervals (RIs) for pediatric patients is crucial in clinical decision-making, and there is a critical gap of pediatric RIs in China. However, the direct sampling technique for establishing RIs is resource-intensive and ethically challenging. Indirect estimation methods, such as unsupervised clustering algorithms, have emerged as potential alternatives for predicting reference intervals. This study introduces deep graph clustering methods into indirect estimation of pediatric reference intervals. Specifically, we propose a Density Graph Deep Embedded Clustering (DGDEC) algorithm, which incorporates a density feature extractor to enhance sample representation and provides additional perspectives for distinguishing different levels of health status among populations. Additionally, we construct an adjacency matrix by computing the similarity between samples after feature enhancement. The DGDEC algorithm leverages the adjacency matrix to capture the interrelationships between patients and divides patients into different groups, thereby estimating reference intervals for the potential healthy population. The experimental results demonstrate that when compared to other indirect estimation techniques, our method ensures the predicted pediatric reference intervals in different age and gender groups are closer to the true values while maintaining good generalization performance. Additionally, through ablation experiments, our study confirms that the similarity between patients and the multi-scale density features of samples can effectively describe the potential health status of patients.

ICPUTRD: Image Cloud Platform for use in tagging and research on decomposition.

Human decomposition studies aim to understand the various factors influencing human decay to assess the deceased and develop postmortem interval (PMI) estimation methods. These types of studies are typically conducted through physical experiments examining the deceased; however, big data systems have the potential to transform how large-scale forensic anthropology research questions can be addressed with curated images of donors with known demographic, climatic, and postmortem historical data. This study introduces ICPUTRD (Image Cloud Platform for Use in Tagging and Research on Decomposition), a web-based software system, which enables forensic scientists to easily access, enhance (or curate), and analyze very large photographic collections documenting the longitudinal process of human decomposition. ICPUTRD, a JavaScript-based application, was designed and built through a combination of the Waterfall and Agile software development life-cycle methods and provides an image search and tagging features with a predefined nomenclature of forensic-related keywords. To evaluate the system, a user study was conducted, involving 27 participants who completed pre- and post-study surveys and three research tasks. Analysis of the study results confirmed the feasibility and practicality of ICPUTRD to facilitate aspects of forensic research and casework involving large collections of digital photographs of human decomposition. It was observed that the nomenclature lacked certain law enforcement keywords, so future work will focus on expanding it to ensure ICPUTRD is suited for all its intended users.

Impacts of crude oil market on global economy: Evidence from the Ukraine-Russia conflict via fuzzy models

The increasing Russia-Ukraine crisis is without a doubt Europe's most prominent conflict since World War II, changing the dynamics of the oil and other key markets. Because the oil market has traditionally interacted with other financial and commodity markets, it will be intriguing to examine how it interacts with substantial financial assets amid market volatility induced by a conflict. The goal of this study is to propose a fuzzy time series (FTS) model and to compare its competitiveness to existing fuzzy time series (FTS) models, Autoregressive Integrated Moving Average (ARIMA) model and some machine learning methods i.e. Artificial Neural Networks (ANN), Support Vector Machine (SVM) and XGBoost models. We considered changes in the partitioning universe of discourse, optimization of parameters method(s), and interval estimation to make the forecast accuracy more precise forecasting than traditional methods via MAPE. The event-based data results show the proposed fuzzy time series model is outperforming all the competitive methods in the study. Furthermore, the proposed model forecasting shows a future decline tendency in WTi market crude oil prices (US$/BBL) after being at the record highest level, which is good news for the worldwide economy.

Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter R = P ( X > Y ) (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique.