Posterior Credible Interval Research Articles

A NICER View of PSR J1231−1411: A Complex Case

Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state (EOS) of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231−1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and EOS analyses, we infer the radius to be 12.6 ± 0.3 km and the mass to be 1.04−0.03+0.05 M ⊙, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. If using an uninformative prior but limited between 10 and 14 km, we find otherwise similar results, but Req=13.5−0.5+0.3 km for the radius. In both cases, we find a nonantipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a noncircular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile.

The Radius of the High-mass Pulsar PSR J0740+6620 with 3.6 yr of NICER Data

We report an updated analysis of the radius, mass, and heated surface regions of the massive pulsar PSR J0740+6620 using Neutron Star Interior Composition Explorer (NICER) data from 2018 September 21 to 2022 April 21, a substantial increase in data set size compared to previous analyses. Using a tight mass prior from radio-timing measurements and jointly modeling the new NICER data with XMM-Newton data, the inferred equatorial radius and gravitational mass are 12.49−0.88+1.28 km and 2.073−0.069+0.069 M ⊙, respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, with an estimated systematic error ≲ 0.1 km. This result was obtained using the best computationally feasible sampler settings providing a strong radius lower limit but a slightly more uncertain radius upper limit. The inferred radius interval is also close to the R=12.76−1.02+1.49 km obtained by Dittmann et al., when they require the radius to be less than 16 km as we do. The results continue to disfavor very soft equations of state for dense matter, with R < 11.15 km for this high-mass pulsar excluded at the 95% probability. The results do not depend significantly on the assumed cross-calibration uncertainty between NICER and XMM-Newton. Using simulated data that resemble the actual observations, we also show that our pipeline is capable of recovering parameters for the inferred models reported in this paper.

Evaluation of three serological tests for the diagnosis of Brucella suis in dogs using Bayesian latent class analysis

Brucella suis infection of dogs is an emerging issue worldwide requiring specific management to address zoonotic risks and animal welfare concerns. Diagnosis in dogs is routinely based on serological testing, but to date these tests have only been validated for use in production animal species and humans. This study aimed to assess the diagnostic performance of three commonly used serological tests in dogs. Canine sera (n = 989) were tested with the Rose Bengal rapid plate agglutination test (RBRPT), the complement fixation test (CFT) and a competitive ELISA (C-ELISA). Diagnostic test performance was evaluated using a three test, two population Bayesian latent class analysis accounting for conditional dependence between the three tests. Positive and negative predictive values (PPV, NPV) were calculated for a range of expected prevalence estimates for the individual tests and test combinations interpreted in series and parallel. The RBRPT showed the highest individual Se of 0.902 (95 % posterior credible interval [PCI] 0.759–0.978) and the CFT the highest individual diagnostic specificity (Sp) of 0.914 (95 % PCI 0.886–0.946). The C-ELISA had marginally the best overall diagnostic performance (Youden’s index = 0.807). The CFT and the C-ELISA interpreted in parallel returned the highest combined Se and Sp (0.988 and 0.885, respectively). All tests returned NPVs of > 0.982 in 2–8 % prevalence settings. Series interpretation of the three-test combination as well as the two-test combinations of the RBRPT and the C-ELISA and the CFT and the C-ELISA produced a PPV of 0.502 when the estimated prevalence was 8 %. While all tests are suitable for the detection of B. suis antibodies in dogs, they should not be interpreted in isolation as their diagnostic value is dependent on the pre-test probability of the disease. As such they are useful tools for the diagnosis of B. suis in dogs when exposure, history and clinical presentation indicate a risk of brucellosis.

Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme

The generalized Pareto distribution plays a significant role in reliability research. This study concentrates on the statistical inference of the generalized Pareto distribution utilizing progressively Type-II censored data. Estimations are performed using maximum likelihood estimation through the expectation–maximization approach. Confidence intervals are derived using the asymptotic confidence intervals. Bayesian estimations are conducted using the Tierney and Kadane method alongside the Metropolis–Hastings algorithm, and the highest posterior density credible interval estimation is accomplished. Furthermore, Bayesian predictive intervals and future sample estimations are explored. To illustrate these inference techniques, a simulation and practical example are presented for analysis.

A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715

We report Bayesian inference of the mass, radius, and hot X-ray emitting region properties—using data from the Neutron Star Interior Composition ExploreR (NICER)—for the brightest rotation-powered millisecond X-ray pulsar, PSR J0437−4715. Our modeling is conditional on informative tight priors on mass, distance, and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA; Reardon et al.), and we use NICER background models to constrain the nonsource background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis, we infer a mass of M = 1.418 ± 0.037 M ⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R=11.36−0.63+0.95 km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be nonantipodal and hence inconsistent with a pure centered dipole magnetic field.

Estimation of diagnostic sensitivity and specificity of abattoir registrations and bulk tank milk ELISA as herd-level tests for Fasciola hepatica using Bayesian latent class modelling

The common liver fluke, Fasciola hepatica, is a trematode parasite found worldwide, typically with a focal distribution due to its requirement for suitable climatic and environmental conditions to complete its lifecycle. Bovine fasciolosis causes suboptimal production and economic losses, including liver condemnation at slaughter. The lack of reliable diagnostic methods is a disadvantage to the increasing demand for surveillance and control. The aim of this study was to evaluate the diagnostic accuracy of bulk tank milk (BTM) antibody testing and aggregated abattoir registrations (AAR) of liver fluke as herd-level tests for F. hepatica infection using Bayesian latent class models. Data from the abattoirs in 2019–2021 and BTM, sampled in the winter of 2020/2021, were collected from 437 herds on the southwest coast of Norway. The BTM samples were analysed with the SVANOVIR® F. hepatica-Ab ELISA test, with results given as an optical density ratio (ODR), and later dichotomized using the recommended cut-off value from the test manufacturer (ODR ≥0.3). Based on the BTM ELISA test, 47.8% of the herds tested positive. The AAR test was defined as the herd-level proportion of female slaughtered animals registered with liver fluke infection during the study period. For this test, three cut-offs were used (a proportion of 0.05, 0.1 and 0.2). The herds were split into two subpopulations (“Coastal” and “Inland”), which were expected to differ in true prevalence of F. hepatica infection based on climate-related and geographical factors. The diagnostic accuracies of both tests were estimated using Bayesian latent class models with minimally informative priors. Post-hoc analysis revealed that the maximum sum of sensitivity (Se) and specificity (Sp) of the tests was achieved with a herd-level proportion of ≥0.1 registered with liver fluke as the AAR test. Using this cut-off, the median estimate for the diagnostic accuracy of the BTM ELISA was 90.4% (84.0–96.2 95% Posterior Credible Interval (PCI)) for Se and 95.3% (90.6–100% PCI) for Sp, while the median estimate of Se for AAR was 87.5% (81.4–93.1% PCI) and the median estimate of Sp for AAR was 91.0% (85.2–96.5% PCI). The cut-off evaluation of the SVANOVIR® F. hepatica-Ab ELISA test for BTM confirmed the manufacturer's recommended cut-off of ODR ≥0.3 to denote positive and negative herds. This study suggests that AAR and BTM ELISA test can be used as herd-level tools to monitor liver fluke infection, so that appropriate interventions against infection can be implemented as necessary.

Simultaneous Confidence Intervals for Ratios of the Percentiles of the Delta-Lognormal Distribution

Statistical percentiles are extremely important and valuable measurement tools in various contexts. They offer significant advantages when it comes to estimating a wide range of values across different fields, making them essential in statistical analysis and research. This importance motivates researchers to study the construction of simultaneous confidence intervals for ratios of percentiles of the delta-lognormal distribution. This research introduces four distinct methods for constructing such confidence intervals: the fiducial generalized confidence interval, the Bayesian-based highest posterior density credible interval using Jeffreys prior, Jeffreys rule prior, and Uniform prior. All methods are subjected to evaluation and comparison through coverage probabilities and expected lengths in Monte Carlo simulations. The simulation study shows that, overall, the Bayesian-based highest posterior density credible interval works better and more accurately than the fiducial generalized confidence interval. To further validate the findings of the simulation study, these methods are applied to real-world daily rainfall data collected from a river basin in Thailand.

Inference of reliability model with burr type XII distribution under two sample balanced progressive censored samples

Abstract The balanced joint progressive censoring scheme gives guidelines for researchers in reducing the expense and period of the experiment with modified efficiency. In this paper, the stress-strength reliability model are considered and investigated, in which two independent samples are generated from Burr Type XII distributions under balanced joint progressive censoring scheme. In the classical analysis, the maximum likelihood estimate of the reliability parameter is derived, then the relevant confidence interval is provided based on the Fisher matrix. Under the Bayesian framework, the Lindley’s technique and hybrid Gibbs within Metropolis-Hastings algorithm are applied to acquire the estimates of the parameters, and the corresponding highest posterior density credible interval of the reliability model is also constructed. The reliability inference is realized by numerical simulation, and the validity of the inference method is analyzed based on the splashing data of silicone oil droplets impact (SSODI) under two surfaces wettability conditions.

Inference of stress-strength reliability based on adaptive progressive type-Ⅱ censing from Chen distribution with application to carbon fiber data

&lt;abstract&gt;&lt;p&gt;In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength $ R = P(Y &amp;lt; X) $ based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of $ R $ was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of $ R $ was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating $ R $ using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of $ R $ and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results.&lt;/p&gt;&lt;/abstract&gt;

Estimating the real burden of gestational syphilis in Brazil, 2007–2018: a Bayesian modeling study

Although several studies have estimated gestational syphilis (GS) incidence in several countries, underreporting correction is rarely considered. This study aimed to estimate the level of under-registration and correct the GS incidence rates in the 557 Brazilian microregions. Brazilian GS notifications between 2007 and 2018 were obtained from the SINAN-Syphilis system. A cluster analysis was performed to group microregions according to the quality of GS notification. A Bayesian hierarchical Poisson regression model was applied to estimate the reporting probabilities among the clusters and to correct the associated incidence rates. We estimate that 45,196 (90%-HPD: 13,299; 79,310) GS cases were underreported in Brazil from 2007 to 2018, representing a coverage of 87.12% (90%-HPD: 79.40%; 95.83%) of registered cases, where HPD stands for the Bayesian highest posterior density credible interval. Underreporting levels differ across the country, with microregions in North and Northeast regions presenting the highest percentage of missed cases. After underreporting correction, Brazil's estimated GS incidence rate increased from 8.74 to 10.02 per 1000 live births in the same period. Our findings highlight disparities in the registration level and incidence rate of GS in Brazil, reflecting regional heterogeneity in the quality of syphilis surveillance, access to prenatal care, and childbirth assistance services. This study provides robust evidence to enhance national surveillance systems, guide specific policies for GS detection disease control, and potentially mitigate the harmful consequences of mother-to-child transmission. The methodology might be applied in other regions to correct disease underreporting. National Council for Scientific and Technological Development; The Bill Melinda Gates Foundation and Wellcome Trust.

Metals and per- and polyfluoroalkyl substances mixtures and birth outcomes in the New Hampshire Birth Cohort Study: Beyond single-class mixture approaches

We aimed to investigate the joint, class-specific, and individual impacts of (i) PFAS, (ii) toxic metals and metalloids (referred to collectively as “metals”), and (iii) essential elements on birth outcomes in a prospective pregnancy cohort using both established and recent mixture modeling approaches. Participants included 537 mother-child pairs from the New Hampshire Birth Cohort Study. Concentrations of 6 metals and 5 PFAS were measured in maternal toenail clippings and plasma, respectively. Birth weight, birth length, and head circumference at birth were abstracted from medical records. Joint, index-wise, and individual associations of the metals and PFAS concentrations with birth outcomes were evaluated using Bayesian Kernel Machine Regression (BKMR) and Bayesian Multiple Index Models (BMIM). After controlling for potential confounders, the metals-PFAS mixture was associated with a larger head circumference at birth, which was driven by manganese. When using BKMR, the difference in the head circumference z-score when changing manganese from its 25th to 75th percentiles while holding all other mixture components at their medians was 0.22 standard deviations (95% posterior credible interval [CI]: −0.02, 0.46). When using BMIM, the posterior mean of index weight estimates assigned to manganese for head circumference z-score was 0.72 (95% CI: 0, 0.99). Prenatal exposure to the metals-PFAS mixture was not associated with birth weight or birth length by either BKMR or BMIM. Using both traditional and new mixture modeling approaches, prenatal exposure to manganese was associated with a larger head circumference at birth after accounting for exposure to PFAS and multiple toxic and essential metals.

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

AbstractIn this paper, we investigate classical and Bayes estimates for stress‐strength reliability (SSR) based on two independent progressive first failure censored samples from beta log Weibull distributions with different shape and scale parameters. The maximum likelihood estimation of SSR and its asymptotic confidence interval are obtained. Bayes estimates of SSR are derived under two different loss functions using the Tierney–Kadane's approximation algorithm. In addition, two different bootstrap confidence intervals are provided and the highest posterior density credible interval of SSR is also constructed by applying Monte Carlo Markov chain method. The performances of different point and interval estimates are assessed using the Monte Carlo simulation. Finally, three real data sets are analyzed for illustration purposes.

Diagnostic Performance of a Machine Learning Algorithm (Asthma/Chronic Obstructive Pulmonary Disease [COPD] Differentiation Classification) Tool Versus Primary Care Physicians and Pulmonologists in Asthma, COPD, and Asthma/COPD Overlap

The differential diagnosis of asthma and chronic obstructive pulmonary disease (COPD) poses a challenge in clinical practice and its misdiagnosis results in inappropriate treatment, increased exacerbations, and potentially death. To investigate the diagnostic accuracy of the Asthma/COPD Differentiation Classification (AC/DC) tool compared with primary care physicians and pulmonologists in asthma, COPD, and asthma-COPD overlap. The AC/DC machine learning-based diagnostic tool was developed using 12 parameters from electronic health records of more than 400,000 patients aged 35 years and older. An expert panel of three pulmonologists and four general practitioners from five countries evaluated 119 patient cases from a prospective observational study and provided a confirmed diagnosis (n= 116) of asthma (n= 53), COPD (n= 43), asthma-COPD overlap (n= 7), or other (n= 13). Cases were then reviewed by 180 primary care physicians and 180 pulmonologists from nine countries and by the AC/DC tool, and diagnostic accuracies were compared with reference to the expert panel diagnoses. Average diagnostic accuracy of the AC/DC tool was superior to that of primary care physicians (median difference, 24%; 95% posterior credible interval: 17% to 29%; P < .0001) and was noninferior and superior (median difference, 12%; 95% posterior credible interval: 6% to 17%; P < .0001 for noninferiority and P= .0006 for superiority) to that of pulmonologists. Average diagnostic accuracies were 73%, 50%, and 61% by AC/DC tool, primary care physicians, and pulmonologists versus expert panel diagnosis, respectively. The AC/DC tool demonstrated superior diagnostic accuracy compared with primary care physicians and pulmonologists in the diagnosis of asthma and COPD in patients aged 35 years and greater and has the potential to support physicians in the diagnosis of these conditions in clinical practice.

Sensitivity and specificity of bacterial culture, qPCR, and somatic cell count for detection of goats with Staphylococcus aureus intramammary infection using Bayesian latent class models

Staphylococcus aureus (S. aureus) is an important udder pathogen affecting goat milk production. The ability to detect goats with subclinical mastitis caused by S. aureus is essential in udder health control programs. In Norway, the industry recommends using somatic cell count (SCC) as a screening tool, and conventional bacterial culture (BC) as a confirmatory test for goat milk samples, but a commercial qPCR, Mastitis 4 qPCR (DNA Diagnostics, Risskov, Denmark) is also available. However, few studies have validated the use of these methods for the detection of goats with S. aureus intramammary infection (IMI). Therefore, the objective of this retrospective study was to estimate the diagnostic sensitivity and specificity of BC, qPCR, and SCC for the detection of goats with IMI caused by S. aureus using Bayesian latent class analysis. We analyzed the BC and qPCR results of aseptically collected milk samples and SCC results from milk recording samples from 319 goats from three herds using different SCC cut-offs. At a SCC cut-off of 2000,000 cells/mL, the estimated median prevalence in each herd was 12.7% (95% highest posterior density credible interval [CI] 6.5–19.8), 15.7% (95% CI 9.3–23.0), and 1.5% (95% CI 0.0–4.3). The median sensitivity was 93.0% (95% CI 80.2–100), 93.6% (95% CI 82.3–100) and 78.2% (95% CI 62.3–91.2) for BC, qPCR, and SCC, respectively. The estimated median specificity of BC was 99.5% (99% CI 98.4–100), for qPCR, 98.9% (95% CI 97.5–100), and for SCC 61.5% (95% CI 56.0–67.1). The results show that BC, which is today’s standard method for diagnosing IMI, has a high accuracy for detection of goats with S. aureus IMI, but qPCR had a sensitivity and specificity similar to BC, and may act as an alternative.

County-Level Social Vulnerability and Breast, Cervical, and Colorectal Cancer Screening Rates in the US, 2018

Area-level factors have been identified as important social determinants of health (SDoH) that impact many health-related outcomes. Less is known about how the social vulnerability index (SVI), as a scalable composite score, can multidimensionally explain the population-based cancer screening program uptake at a county level. To examine the geographic variation of US Preventive Services Task Force (USPSTF)-recommended breast, cervical, and colorectal cancer screening rates and the association between county-level SVI and the 3 screening rates. This population-based cross-sectional study used county-level information from the Centers for Disease Control and Prevention's PLACES and SVI data sets from 2018 for 3141 US counties. Analyses were conducted from October 2021 to February 2022. Social vulnerability index score categorized in quintiles. The main outcome was county-level rates of USPSTF guideline-concordant, up-to-date breast, cervical, and colorectal screenings. Odds ratios were calculated for each cancer screening by SVI quintile as unadjusted (only accounting for eligible population per county) or adjusted for urban-rural status, percentage of uninsured adults, and primary care physician rate per 100 000 residents. Across 3141 counties, county-level cancer screening rates showed regional disparities ranging from 54.0% to 81.8% for breast cancer screening, from 69.9% to 89.7% for cervical cancer screening, and from 39.8% to 74.4% for colorectal cancer screening. The multivariable regression model showed that a higher SVI was significantly associated with lower odds of cancer screening, with the lowest odds in the highest SVI quintile. When comparing the highest quintile of SVI (SVI-Q5) with the lowest quintile of SVI (SVI-Q1), the unadjusted odds ratio was 0.86 (95% posterior credible interval [CrI], 0.84-0.87) for breast cancer screening, 0.80 (95% CrI, 0.79-0.81) for cervical cancer screening, and 0.72 (95% CrI, 0.71-0.73) for colorectal cancer screening. When fully adjusted, the odds ratio was 0.92 (95% CrI, 0.90-0.93) for breast cancer screening, 0.87 (95% CrI, 0.86-0.88) for cervical cancer screening, and 0.86 (95% CrI, 0.85-0.88) for colorectal cancer screening, showing slightly attenuated associations. In this cross-sectional study, regional disparities were found in cancer screening rates at a county level. Quantifying how SVI associates with each cancer screening rate could provide insight into the design and focus of future interventions targeting cancer prevention disparities.

Evaluation of three commercial ELISA tests for serological detection of maedi-visna virus using Bayesian latent class analysis

Early and accurate diagnosis is fundamental for successful surveillance and control of maedi-visna virus (MVV). MVV was detected in Norway in 2019, almost 14 years after the previous outbreak. Genetic analysis indicates persistence of the virus in the sheep population since 2005. The virus was not detected despite continuous serological surveillance. This emphasises the need for improved surveillance, which relies on an understanding of both diagnostic test performance, sampling strategy and the prevalence of the disease. This study therefore aims to evaluate three commercial ELISA tests for MVV antibodies. We conducted a retrospective study using 615 samples from six flocks diagnosed with MVV in 2019. We ran all samples with the following three tests: ID Screen® MVV/CAEV Indirect (IDvet, Grabels, France), IDEXX MVV/CAEV p28 Ab Verification Test (IDEXX Laboratories, Maine, USA) and Elitest MVV/CAEV (Hyphen Biomed, Neuville-sur-Oise, France), hereinafter referred to as ID Screen, IDEXXp28 and Elitest respectively. Without a perfect reference test, we used Bayesian latent class analysis, including conditional dependence between tests, to estimate diagnostic accuracy and true prevalence in the flocks. Using recommended cut-off values, we found that ID Screen and Elitest had significantly higher sensitivity (Se) estimates (99.3 % [97.4–100.0, 95 % Posterior Credible Interval] and 97.4 % [94.1–99.7 %], respectively) than IDEXXp28 (79.5 % [72.3–86.0 %]), while IDEXXp28 and ID Screen had significantly higher specificity (Sp) estimates than Elitest (99.7 % [99.1–100.0], 99.1 % [98.0–99.8 %] and 93.7 % [91.4–95.7 %], respectively). The estimated true prevalence in the six flocks ranged from a median of 0.8–93.5 %. Combining ID Screen and Elitest in serial interpretation showed the highest median Se and Sp (96.7 % [92.0–99.1] and 100.0 % [99.9–100.0], respectively), as well as the highest median positive predictive value (PPV) for the population with the lowest prevalence. Our study supports the use of ID Screen for screening. Further verification with Elitest in serial interpretation will enhance the PPV.

Inference for reliability in a multicomponent stress-strength model from generalized inverted exponential lifetime distribution under progressive first failure censoring

This article considers the non-Bayesian and Bayesian estimation procedures for multicomponent stress-strength reliability (MSSR) from generalized inverted exponential lifetime distributions using a progressively first failure censoring scheme. For the non-Bayesian estimation method of MSSR, the maximum likelihood estimation method is used, and for the Bayesian estimation method, the Metropolis-Hastings algorithm is taken into account. Also, the highest posterior density credible interval and the asymptotic confidence interval for MSSR in the case of Bayesian and non-Bayesian estimation methods, respectively, are obtained. A Monte Carlo numerical study is conducted to compare different types of estimates. For illustrative purposes, a real data analysis is carried out.

Estimating reliability parameters for inverse Gaussian distributions under complete and progressively type-II censored samples

ABSTRACT In this paper, we study estimation of stress-strength reliability, assuming the stress and strength variables are inverse Gaussian distributed with unknown parameters. When the coefficient of variations of the distributions is unknown but equal, we develop MLE, Bayes estimator, bootstrap interval of the reliability. The profile likelihood Bayes estimator of the coefficient of variation is also derived. When all parameters are different, we derive the MLE, UMVUE, Bayes estimator, bootstrap interval, and highest posterior density credible interval of the stress-strength reliability. The predictive Bayes estimators of the reliability functions are derived. Under progressive type-II censoring, we derive the MLE, Bayes estimator and bootstrap confidence interval. Monte-Carlo simulation results and real data-based examples are also presented. We analyze lung cancer and air pollution data sets as applications of the stress-strength model.

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

Multicomponent Stress-Strength Model Based on Generalized Progressive Hybrid Censoring Scheme: A Statistical Analysis.

The statistical inference of the reliability and parameters of the stress–strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress–strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton–Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI). Subsequently, the exact confidence interval (ECI) of the parameters was calculated. A hybrid Markov chain Monte Carlo (MCMC) method was adopted to determine the approximate Bayesian estimation (BE) of the unknown parameters and the high posterior density credible interval (HPDCI). A simulation study with the actual dataset was conducted for the BEs with squared error loss function (SELF) and the MLEs of the model parameters and reliability, comparing the bias and mean squares errors (MSE). In addition, the three interval estimates were compared in terms of the average interval length (AIL) and coverage probability (CP).