Credible Confidence Intervals Research Articles

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients.

Constant-Stress Partially Accelerated Life Testing for Weibull Inverted Exponential Distribution with Censored Data

The novelty of this article is estimating the parameters of Weibull inverted exponential (WIE)distribution with a constant stress partially accelerated life test (PALT) under adaptive type-II progressivelycensored samples. Moreover, the maximum likelihood estimators (MLEs), their asymptotic variances confidenceintervals, and Bayes estimators (BEs) of the model parameters and the acceleration factor are obtained.Furthermore, the approximate bootstrap and credible confidence intervals of the estimators are acquired. Theaccuracy of the MLEs and BEs for the model parameters and the acceleration factor is investigated through thesimulation studies.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

The current research offers an enhanced three-parameter lifetime model that combines the unit Burr XII distribution with a power series distribution. The novel class of distribution is named the unit Burr XII power series (UBXIIPS). This compounding technique allows for the production of flexible distributions with strong physical meanings in domains such as biology and engineering. The UBXIIPS class includes the unit Burr XII Poisson (UBXIIP) distribution, the unit Burr XII binomial distribution, the unit Burr XII geometric distribution, and the unit Burr XII negative binomial distribution. The statistical properties of the class include formulas for the density and cumulative distribution functions, and limiting behaviour, moments and incomplete moments, entropy measures, and quantile function are provided. For estimating population parameters and fuzzy reliability for the UBXIIP model, maximum likelihood and Bayesian approaches are studied by the Metropolis–Hastings algorithm. For maximum likelihood estimators, the length of asymptotic confidence intervals is specified, whereas, for Bayesian estimators, the length of credible confidence intervals is assigned. A simulation investigation of the UBXIIP model was established to evaluate the performance of suggested estimates. In addition, the UBXIIP distribution is explored using real-world data. The UBXIIP distribution appears to offer some benefits in understanding lifetime data when compared to unit Weibull, beta, Kumaraswamy, Kumaraswamy Kumaraswamy, Marshall-Olkin Kumaraswamy, and Topp–Leone Weibull Lomax distributions.

Reliability analysis of two Gompertz populations under joint progressive type-ii censoring scheme based on binomial removal

ABSTRACT Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies.

On Statistical Inference of Generalized Pareto Distribution with Jointly Progressive Censored Samples with Binomial Removal

A jointly censored sample is a very useful sampling technique in conducting comparative life tests of the products, its efficiency appears in permitting the selection of two samples from two manufacturing lines at the same time and conducting a life‐testing experiment. This article presents estimation information of the joint generalized Pareto distributions parameters using Type‐II progressive censoring scheme, which is carried out with binomial removal. The generalized Pareto distribution has many applications in different fields. We outline the problem of parameter estimation using the frequentest maximum likelihood and the Bayesian estimation methods. Furthermore, different interval estimation methods for estimating the four parameters were used: the asymptotic property of the maximum likelihood estimator, the credible confidence intervals, and the Bootstrap confidence intervals. The detailed numerical simulations have been considered to compare the performance of the proposed estimates. In addition, the applicability of the joint generalized Pareto censored model has been performed by applying a real data example.

Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode

Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods.

The new discrete distribution with application to COVID-19 Data

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall–Olkin family and the inverse Toppe–Leone distribution, both of them were used to introduce a new discrete distribution called Marshall–Olkin inverse Toppe–Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall–Olkin Inverse Toppe–Leone (DMOITL). This new model possesses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte-Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).

Inference for a constant-stress model under progressive type-I interval censored data from the generalized half-normal distribution

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed.

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

On Step-Stress Accelerated Life Testing for Power Generalized Weibull Distribution Under Progressive Type-II Censoring

In this paper, step-stress accelerated life testing is studied when the lifetime of test units follows power generalized Weibull distribution (PGW). Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained under type-II progressive censoring. Moreover, the approximate and credible confidence intervals of the parameters are derived. Also, simulation studies are conducted to check the precision of the MLEs and BEs for the parameters of PGW distribution. Finally, some interesting conclusions are obtained.

Indirect Effects in Sequential Mediation Models: Evaluating Methods for Hypothesis Testing and Confidence Interval Formation

Complex mediation models, such as a two-mediator sequential model, have become more prevalent in the literature. To test an indirect effect in a two-mediator model, we conducted a large-scale Monte Carlo simulation study of the Type I error, statistical power, and confidence interval coverage rates of 10 frequentist and Bayesian confidence/credible intervals (CIs) for normally and nonnormally distributed data. The simulation included never-studied methods and conditions (e.g., Bayesian CI with flat and weakly informative prior methods, two model-based bootstrap methods, and two nonnormality conditions) as well as understudied methods (e.g., profile-likelihood, Monte Carlo with maximum likelihood standard error [MC-ML] and robust standard error [MC-Robust]). The popular BC bootstrap showed inflated Type I error rates and CI under-coverage. We recommend different methods depending on the purpose of the analysis. For testing the null hypothesis of no mediation, we recommend MC-ML, profile-likelihood, and two Bayesian methods. To report a CI, if data has a multivariate normal distribution, we recommend MC-ML, profile-likelihood, and the two Bayesian methods; otherwise, for multivariate nonnormal data we recommend the percentile bootstrap. We argue that the best method for testing hypotheses is not necessarily the best method for CI construction, which is consistent with the findings we present.

Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data

The Burr Type XII distribution has been widely applied in the real data analysis. In the censored data modeling, adopting the efficient parameter estimation methods and then predicting the censored observation are very important. In this paper, the parameters estimation and prediction of the Burr Type XII distribution under the doubly censoring scheme are studied. The maximum likelihood estimates of the unknown parameters are earned through the Expectation–Maximization (EM) algorithm. Since the Bayes estimators cannot be evaluated in explicit form, we propose to apply the Tierney and Kadane’s and Markov Chain Monte Carlo procedure to approximate them. The asymptotic and the highest posterior density credible confidence intervals for the unknown parameters are introduced. Based on the Monte Carlo simulations, different proposed estimators are compared. The predictive intervals of the future observation are also constructed. Finally, the proposed methods have been studied using the two real microfluidics data.

Inference on Constant-Stress Accelerated Life Testing Based on Geometric Process for Extension of the Exponential Distribution under Type-II Progressive Censoring

In this paper, the geometric process is introduced as a constant-stress accelerated model to analyze a series of life data that obtained from several increasing stress levels. The geometric process (GP) model is assumed when the lifetime of test units follows an extension of the exponential distribution. Based on progressive censoring, the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. Moreover, a real dataset is analyzed to illustrate the proposed procedures. In addition, the approximate, bootstrap and credible confidence intervals (CIs) of the estimators are constructed. Finally, simulation studies are carried out to investigate the precision of the MLEs and BEs for the parameters involved.

Venous Thromboembolism Risk in Head and Neck Cancer: Significance of the Preoperative Platelet-to-Lymphocyte Ratio.

Objective We aimed to investigate the association between the preoperative platelet-to-lymphocyte ratio (PLR) and venous thromboembolism (VTE) in patients with head and neck cancer (HNC) undergoing major surgery. Study Design Retrospective cohort study. Setting Academic tertiary hospital from 2011 to 2017. Subjects and Methods Patients with confirmed HNC undergoing major surgery were included in this study. The preoperative PLR was recorded for all patients. Known VTE risk factors, including Caprini score, age, sex, smoking, body mass index, prior VTE, and anticoagulation, were also recorded. Risk factors were screened in univariate analysis using Wilcoxon's rank sum test and χ2 test (Bonferroni corrected). Significant covariates were included in a multivariate regression model. Bootstrap techniques were used to obtain credible confidence intervals (CIs). Results There were 306 patients enrolled with 7 cases of VTE (6 deep vein thromboses and 1 pulmonary embolism. On univariate analysis, length of stay ( P = .0026), length of surgery ( P = .0029), and PLR ( P = .0002) were found to have significant associations with VTE. A receiver operator characteristic (ROC) curve was constructed that yielded an area under the ROC of 0.905 (95% CI, 0.82-0.98). Using an optimized cutoff, the multivariate model showed that length of surgery (β 95% CI, 0.0001-0.0006; P = .0056) and PLR (β 95% CI, 5.3256-5.3868; P < .0001) were significant independent predictors of VTE. Conclusion This exploratory pilot study has shown that PLR offers a potentially accurate risk stratification measure as an adjunct to current tools in VTE risk prediction, without additional cost to health systems.

Classical and Bayesian inference on progressive‐stress accelerated life testing for the extension of the exponential distribution under progressive type‐II censoring

AbstractIn this paper, a progressive‐stress accelerated life test under progressive type‐II censoring is considered. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. The maximum likelihood and Bayes estimates of the model parameters are obtained. The approximate and credible confidence intervals of the estimators are derived. Furthermore, a real lifetime data set is analyzed to illustrate the proposed procedures. Finally, the simulation studies are used to compare between 2 different designs of the progressive‐stress test (simple and multiple ramp‐stress tests).

A Neighborhood-Wide Association Study (NWAS): Example of prostate cancer aggressiveness.

PurposeCancer results from complex interactions of multiple variables at the biologic, individual, and social levels. Compared to other levels, social effects that occur geospatially in neighborhoods are not as well-studied, and empiric methods to assess these effects are limited. We propose a novel Neighborhood-Wide Association Study(NWAS), analogous to genome-wide association studies(GWAS), that utilizes high-dimensional computing approaches from biology to comprehensively and empirically identify neighborhood factors associated with disease.MethodsPennsylvania Cancer Registry data were linked to U.S. Census data. In a successively more stringent multiphase approach, we evaluated the association between neighborhood (n = 14,663 census variables) and prostate cancer aggressiveness(PCA) with n = 6,416 aggressive (Stage≥3/Gleason grade≥7 cases) vs. n = 70,670 non-aggressive (Stage<3/Gleason grade<7) cases in White men. Analyses accounted for age, year of diagnosis, spatial correlation, and multiple-testing. We used generalized estimating equations in Phase 1 and Bayesian mixed effects models in Phase 2 to calculate odds ratios(OR) and confidence/credible intervals(CI). In Phase 3, principal components analysis grouped correlated variables.ResultsWe identified 17 new neighborhood variables associated with PCA. These variables represented income, housing, employment, immigration, access to care, and social support. The top hits or most significant variables related to transportation (OR = 1.05;CI = 1.001–1.09) and poverty (OR = 1.07;CI = 1.01–1.12).ConclusionsThis study introduces the application of high-dimensional, computational methods to large-scale, publically-available geospatial data. Although NWAS requires further testing, it is hypothesis-generating and addresses gaps in geospatial analysis related to empiric assessment. Further, NWAS could have broad implications for many diseases and future precision medicine studies focused on multilevel risk factors of disease.

Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring

In this paper, constant-stress accelerated life test is assumed when the lifetime of test units follows an extension of the exponential distribution. Based on progressive censoring, the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. The BEs are obtained based on both non-informative and informative priors. In addition, the approximate, bootstrap and credible confidence intervals (CIs) of the estimators are constructed. Moreover, a real dataset is analyzed to illustrate the proposed procedures. Furthermore, the real dataset is used to show that extension of the exponential distribution can be a better model than Weibull distribution and generalized exponential distribution. Finally, simulation studies are carried out to investigate the accuracy of the MLEs and BEs for the parameters involved.

Assessment of Random Error in Phantom Dosimetry with the Use of Error Simulation in Statistical Software.

Objective. To investigate if software simulation is practical for quantifying random error (RE) in phantom dosimetry. Materials and Methods. We applied software error simulation to an existing dosimetry study. The specifications and the measurement values of this study were brought into the software (R version 3.0.2) together with the algorithm of the calculation of the effective dose (E). Four sources of RE were specified: (1) the calibration factor; (2) the background radiation correction; (3) the read-out process of the dosimeters; and (4) the fluctuation of the X-ray generator. Results. The amount of RE introduced by these sources was calculated on the basis of the experimental values and the mathematical rules of error propagation. The software repeated the calculations of E multiple times (n = 10,000) while attributing the applicable RE to the experimental values. A distribution of E emerged as a confidence interval around an expected value. Conclusions. Credible confidence intervals around E in phantom dose studies can be calculated by using software modelling of the experiment. With credible confidence intervals, the statistical significance of differences between protocols can be substantiated or rejected. This modelling software can also be used for a power analysis when planning phantom dose experiments.