Posterior Risks Research Articles

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

A Bayesian design method for monopropellant engine system reliability qualification test plan

During the development of systems, traditional System Reliability Qualification Testing (SRQT) is typically utilized to assess whether they meet predefined reliability standards. However, this approach often demands substantial sample sizes and prolonged test durations, rendering it impractical for costly, highly reliable systems with limited sample sizes. Additionally, the extended test duration may not align with practical time-to-market pressures or budget constraints. To overcome these challenges, the study integrates subsystem data into the monopropellant engine system RQT plan's design. By leveraging Monte-Carlo simulation, subsystem data is modeled to create a system parameter distribution, enabling the formulation of SRQT plans based on posterior risks. An example of a monopropellant liquid rocket engine system is provided to demonstrate the advantages and applications of the proposed methodology.

The 3-component mixture of power distributions under Bayesian paradigm with application of life span of fatigue fracture

Mixture distributions are naturally extra attractive to model the heterogeneous environment of processes in reliability analysis than simple probability models. This focus of the study is to develop and Bayesian inference on the 3-component mixture of power distributions. Under symmetric and asymmetric loss functions, the Bayes estimators and posterior risk using priors are derived. The presentation of Bayes estimators for various sample sizes and test termination time (a fact of time after that test is terminated) is examined in this article. To assess the performance of Bayes estimators in terms of posterior risks, a Monte Carlo simulation along with real data study is presented.

Dynamic Weighted Cumulative Residual Entropy Estimators for Laplace Distribution: Bayesian Approach

Objectives: To develop Bayesian estimators of dynamic weighted cumulative residual entropy (DWCRE) for Laplace distribution and to investigate posterior risks using various priors and loss functions. Methods: Weighted entropy measure of information is provided by a probabilistic experiment whose basic events are described by their objective probabilities and some qualitative (objective or subjective) weights. In this paper, we have used priors (Jeffrey’s, Hartigan, Uniform and Gumble Type II) and several loss functions. Findings: Bayesian estimators and associated posterior risks for Laplace distribution have been derived for different priors and loss functions. Monte Carlo Simulation study and graphical analyses have also been presented along with the conclusion. Through the comprehensive simulation study in the paper, it has been observed that Hartigan prior is better than other priors in terms of the posterior risk whereas Uniform prior has always higher posterior risk. Novelty: The introduction of new Bayesian estimators and their posterior risks for dynamic weighted cumulative residual entropy (DWCRE) of Laplace distribution. Keywords: Bayesian estimators, Laplace distribution, Fisher information matrix, Loss functions, Priors

Arsenic in drinking water and lung cancer: A systematic review of 35 years of evidence

The association between higher arsenic concentrations in drinking water and lung cancer is well-established. However, the risk associated with lower levels of arsenic exposure remains uncertain. This systematic review and meta-analysis summarizes the evidence on the relationship between exposure to arsenic in drinking water and lung cancer outcomes as measured over a broad range of exposures, including lower levels. A total of 51 studies were included in the review and 15 met criteria for inclusion in meta-analysis. Risk estimates for lung cancer incidence and mortality were pooled and analyzed separately using Bayesian hierarchical random-effects models with a Gaussian observation submodel for log(Risk), computed using the “brms” R package. For lung cancer incidence, the predicted posterior mean relative risks (RRs) at arsenic concentrations of 10, 50 and 150 μg/L were 1.11 (0.86–1.43), 1.67 (1.27–2.17) and 2.21 (1.61–3.02), respectively, with posterior probabilities of 79%, 100% and 100%, respectively, for the RRs to be >1. The posterior mean mortality ratios at 20, 50 and 150 μg/L were 1.22 (0.83–1.78), 2.10 (1.62–2.71) and 2.41 (1.88–3.08), respectively, with posterior probabilities being above 80%. In addition to observing the dose-response relationship, these findings demonstrate that individuals exposed to low to moderate levels of arsenic (<150 μg/L) were at an elevated risk of developing or dying from lung cancer. Given the widespread exposure to lower levels of arsenic, there is an urgent need for vigilance and potential revisions to regulatory guidelines to protect people from the cancer risks associated with arsenic exposure.

Reliability analysis for two populations Nadarajah-Haghighi distribution under Joint progressive type-II censoring

&lt;abstract&gt;&lt;p&gt;In order to evaluate the competitive advantages and dependability of two products in a competitive environment, comparative lifespan testing becomes essential. We examine the inference problems that occur when two product lines follow the Nadarajah-Haghighighi distribution in the setting of joint type-II censoring. In the present study, we derived the maximum likelihood estimates for the Nadarajah-Haghighi population parameters. Additionally, a Fisher information matrix was constructed based on these maximum likelihood estimations. Furthermore, Bayesian estimators and their corresponding posterior risks were calculated, considering both gamma and non-informative priors under symmetric and asymmetric loss functions. To assess the performance of the overall parameter estimators, we conducted a Monte Carlo simulation using numerical methods. Lastly, a real data analysis was carried out to validate the accuracy of the models and methods discussed.&lt;/p&gt;&lt;/abstract&gt;

Arsenic in Drinking Water and Urinary Tract Cancers: A Systematic Review Update

Problem: There remains uncertainty around cancer risk at lower levels of arsenic in drinking water. This study updates evidence from our previous review on the relationship between arsenic in drinking water and urinary bladder and kidney cancers (updated search January 2013 to February 2023). Method: Thirty-four studies were retained for review; six met criteria for inclusion in meta-analysis. Risk estimates for bladder and kidney cancer incidence and mortality were analyzed separately using Bayesian multilevel linear models. Results: For bladder cancer incidence, the estimated posterior mean relative risks (RRs) were 1.25 (0.92–1.73), 2.11 (1.18–4.22) and 3.01 (1.31–8.17) at arsenic concentrations of 10, 50 and 150 μg/L, respectively, with posterior probabilities of 92%, 99% and 100%, respectively, for the RRs to be &gt;1. The corresponding RRs for kidney cancer were 1.37 (1.07–1.77), 1.95 (1.44–2.65) and 2.47 (1.74–3.52), with posterior probabilities of 100%. For bladder cancer, the posterior mean mortality ratios were 1.36 (0.35–6.39), 2.92 (1.24–7.82) and 4.88 (2.83–9.03) with posterior probabilities of 72%, 99% and 100%, respectively. Conclusions: The findings show increased bladder and kidney cancer risks at lower levels of arsenic in drinking water. Given that many people worldwide are exposed to lower levels of arsenic in drinking water, the public health impacts are substantial.

Statistical Inference for Two Gumbel Type-II Distributions under Joint Type-II Censoring Scheme

Comparative lifetime tests are extremely significant when the experimenters study the reliability of the comparative advantages of two products in competition. Considering joint type-II censoring, we deal with the inference when two product lines conform to two Gumbel type-II distributions. The maximum likelihood estimations of Gumbel type-II population parameters were obtained in the current research. An approximate confidence interval and a simultaneous confidence interval based on a Fisher information matrix were also constructed and compared with two bootstrap confidence intervals. Moreover, to evaluate the influence of the prior information, based on the concept of importance sampling, we calculated the Bayesian estimator together with their posterior risks in the case of gamma and non-informative priors under different loss functions. To compare the performances of the overall parameters’ estimator, a Monte Carlo simulation was performed using numerical and graphical methods. Finally, a real data analysis was conducted to verify the accuracy of all the models and methods mentioned.

BAYESIAN ANALYSIS UNDER UNBALANCED AND BALANCED LOSS FUNCTIONS APPLYING DIFFERENT PRIOR INFORMATIONS

In this paper, We perform a Bayesian analysis of Zeghdoudi distribution based on type II censored data. Using two type of loss functions; balanced and unbalanced loss functions, we use three different loss functions. this estimation includes three cases of prior informations; availability and lack of primary information, we obtain Bayes estimators and the corresponding posterior risks. the analytical forms of these estimators are out of reach, so, we propose Markov chain Monte-Carlo (MCMC) procedure. Moreover, given initial values for the parameters of the model,we obtain maximum likelihood estimators. Furthermore, we compare their performance with those of the Bayesian estimators using balanced and unbalanced loss functions.

A note on the posterior risk of the entropy loss function

Scholars have discussed the Bayesian estimation and their corresponding posterior risks for the Lindley distribution parameter, respectively, using seven different loss functions, where the posterior risk under entropy loss function (ELF) is not correct. In this paper, we will derive the Bayesian estimation and its corrected posterior risk under the entropy loss function. Moreover, the Bayesian estimations and their posterior risks of binomial distribution parameter under the entropy loss function and squared error loss function are respectively developed. Monte Carlo simulation example and application example are provided for illustrative purposes, and results are compared based on posterior risk.

Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

This paper explores the Lomax-Gumbel {Frechet} distribution in the Bayesian paradigm. The posterior distributions of the parameters are not attained in closed form, so the Lindley and the Tierney-Kadane approximation methods are used for the evaluation of Bayes estimators and associated posterior risks under uniform, Maxwell, and half logistic priors. A complete implementation of these two techniques is provided. Three loss functions are used. An extensive simulation study and two real life data are provided to obtain and compare Bayes estimators in terms of prior distributions and loss functions. It is reported that the Bayes estimators obtained through the Tierney-Kadane method give better results than the Lindley approximation method, in terms of minimum posterior risks.

Bayesian Estimation of Transmuted Lomax Mixture Model with an Application to Type-I Censored Windshield Data

Transmuted distributions have been centered of focus for researchers recently due to their flexibility and applicability in statistics. However, the only few contributions have considered estimation for mixture of transmuted lifetime models especially under Bayesian methods has been explored more recently. We have considered the Bayesian estimation of transmuted Lomax mixture model (TLMM) for type-I censored samples. The Bayes estimates (BEs) for informative and non-informative priors. The BEs and posterior risks (PRs) are evaluated using four different loss functions (LFs), two symmetric and two asymmetric, namely the squared error loss function (SELF), precautionary loss function (PLF), weighted balance loss function (WBLF), and general entropy loss function (GELF). Simulations are run using Lindley Approximation method to compare the BEs under various sample sizes and censoring rates. The estimates under informative prior and GELF were found superior to their counterparts. The applicability of the proposed estimates has been illustrated using the analysis of a real data regarding type-I censored failure times of windshields airplanes.

Bayesian Estimators of Dynamic Cumulative Residual Entropy for Pareto Type II Distribution

In this paper, Pareto type II distribution is used to propose Bayes estimator of dynamic cumulative residual entropy. To calculate posterior risks, various informative and non-informative priors are used. Using different loss functions, Bayes estimators and associated posterior risks for the distribution have been calculated. Numerical computation is carried out with the help of a real dataset. In the last, Monte Carlo Simulation study and Graphical analysis are also given along with the conclusion drawn.

Small area disease mapping of cancer incidence in British Columbia using Bayesian spatial models and the smallareamapp R Package.

There is an increasing interest in small area analyses in cancer surveillance; however, technical capacity is limited and accessible analytical approaches remain to be determined. This study demonstrates an accessible approach for small area cancer risk estimation using Bayesian hierarchical models and data visualization through the smallareamapp R package. Incident lung (N = 26,448), female breast (N = 28,466), cervical (N = 1,478), and colorectal (N = 25,457) cancers diagnosed among British Columbia (BC) residents between 2011 and 2018 were obtained from the BC Cancer Registry. Indirect age-standardization was used to derive age-adjusted expected counts and standardized incidence ratios (SIRs) relative to provincial rates. Moran's I was used to assess the strength and direction of spatial autocorrelation. A modified Besag, York and Mollie model (BYM2) was used for model incidence counts to calculate posterior median relative risks (RR) by Community Health Service Areas (CHSA; N = 218), adjusting for spatial dependencies. Integrated Nested Laplace Approximation (INLA) was used for Bayesian model implementation. Areas with exceedance probabilities (above a threshold RR = 1.1) greater or equal to 80% were considered to have an elevated risk. The posterior median and 95% credible intervals (CrI) for the spatially structured effect were reported. Predictive posterior checks were conducted through predictive integral transformation values and observed versus fitted values. The proportion of variance in the RR explained by a spatial effect ranged from 4.4% (male colorectal) to 19.2% (female breast). Lung cancer showed the greatest number of CHSAs with elevated risk (Nwomen = 50/218, Nmen = 44/218), representing 2357 total excess cases. The largest lung cancer RRs were 1.67 (95% CrI = 1.06-2.50; exceedance probability = 96%; cases = 13) among women and 2.49 (95% CrI = 2.14-2.88; exceedance probability = 100%; cases = 174) among men. Areas with small population sizes and extreme SIRs were generally smoothed towards the null (RR = 1.0). We present a ready-to-use approach for small area cancer risk estimation and disease mapping using BYM2 and exceedance probabilities. We developed the smallareamapp R package, which provides a user-friendly interface through an R-Shiny application, for epidemiologists and surveillance experts to examine geographic variation in risk. These methods and tools can be used to estimate risk, generate hypotheses, and examine ecologic associations while adjusting for spatial dependency.

On ranking climate factors affecting the living organisms based on paired comparison model, a Bayesian approach

The method of paired comparisons (PC) endeavors to rank treatments presented in pairs to panelists (or respondents, judges, jurists, etc.) and they have to select the better one based on sensory evaluations. Sometimes the situations may occur when the panelists cannot discriminate between the treatments and declare a tie. In this study, an effort is made to extend the Weibull PC model to accommodate ties. The extended Weibull PC model is analyzed using Bayesian paradigm. Four different loss functions are used under noninformative (Uniform and Jeffreys) priors. The posterior and marginal posterior distributions are derived. The posterior estimates, posterior risks, preference probabilities, posterior probabilities and predictive probabilities are evaluated to know the ranking of ecological factor. The goodness of the proposed model is assessed. The entire analysis is carried out using a real data set based on the preference for the ecological factors.

Large Reduction in Postoperative Posterior Tibial Slope Risks Anterior Collapse of the Tibial Component in Fixed-Bearing Unicompartmental Knee Arthroplasty

BackgroundAlthough the posterior tibial slope (PTS) of the tibial component in unicompartmental knee arthroplasty is recommended to be between 3° and 7°, variations in preoperative PTS are wide. The purpose of this study was to evaluate the influence of the changes in preoperative and postoperative PTS on clinical outcomes. MethodsOne-hundred and eighty-two knees that underwent medial fixed-bearing unicompartmental knee arthroplasty were evaluated retrospectively. The mean follow-up period was 36.4 ± 13.2 months (range, 24 to 63 months). Preoperative and postoperative PTS were measured on lateral radiographs. Knees were classified in the large reduction group if the postoperative PTS was reduced by more than 5° compared with the preoperative value and in the small reduction group if not. Knee flexion angle and 2011 Knee Society Knee Scoring System were evaluated at the last follow-up of at least 2 years. ResultsThirty-three knees were classified in the large reduction group, and 149 knees were classified in the small reduction group. The preoperative and postoperative PTS of large and small reduction groups were 10.9 ± 2.2, 3.6 ± 2.4 degrees and 7.7 ± 2.7, 7.1 ± 2.4 degrees, respectively. Flexion angle and 2011 Knee Society Knee Scoring System were not significantly different between the groups. However, the incidence of anterior collapse of the tibial component in the large group was significantly higher than that in the other group (P < .001). ConclusionsLarge reduction in the postoperative PTS may be associated with anterior tibial collapse, and therefore this study shows one potential benefit for matching native slope.

Integrated model of health risk assessment for workers having to work outdoors under exposure to cooling meteorological factors

Natural resources extraction involves continuous exposure to cooling meteorological factors typical for open production grounds. This necessitates relevant health risk assessment and management of health risks caused by exposure to these harmful occupational factors. However, the available risk assessment models do not provide a possibility to perform complete assessment of the existing risks created by exposure to meteorological hazards. The study design included the following. We performed hygienic assessment of working conditions and health of workers employed by “Samotlorneftegaz” Joint Stock Company (JSC) who had to perform their work tasks under exposure to cooling meteorological factors on open production grounds; the assessment involved calculating the group health risk. Individual peculiarities were assessed using subjective (547 people took part in questioning) and objective assessment methods (76 people took part in estimating thermal state of their bodies and 54 people participated in thermometry with cold stress). Finally, we assessed prior and posterior risks. The prior group risk assessment made it possible to identify risk groups who had a significant risk of developing occupational and non-occupational diseases and to rank working places as per health hazards. The posterior risk assessment confirmed the results produced by the prior risk assessment regarding potentiating negative effects produced by cooling meteorological factors. The assessment of developing general and local thermoregulation disorders revealed that certain individual peculiarities made a substantial contribution into their development. Among them, we can mention long-term outdoor work (60 % of work time or more) under exposure to cooling meteorological factors; a chronic pathology; tobacco smoking. The results produced by this study allowed us to suggest an integrated model for risk assessment, management and communication about health risks caused by working under exposure to cooling meteorological factors.

Комплексная модель оценки риска нарушений здоровья при работе на открытой территории в условиях воздействия охлаждающих метеорологических факторов

Natural resources extraction involves continuous exposure to cooling meteorological factors typical for open production grounds. This necessitates relevant health risk assessment and management of health risks caused by exposure to these harmful occupational factors. However, the available risk assessment models do not provide a possibility to perform complete assessment of the existing risks created by exposure to meteorological hazards. The study design included the following. We performed hygienic assessment of working conditions and health of workers employed by “Samotlorneftegaz” Joint Stock Company (JSC) who had to perform their work tasks under exposure to cooling meteorological factors on open production grounds; the assessment involved calculating the group health risk. Individual peculiarities were assessed using subjective (547 people took part in questioning) and objective assessment methods (76 people took part in estimating thermal state of their bodies and 54 people participated in thermometry with cold stress). Finally, we assessed prior and posterior risks. The prior group risk assessment made it possible to identify risk groups who had a significant risk of developing occupational and non-occupational diseases and to rank working places as per health hazards. The posterior risk assessment confirmed the results produced by the prior risk assessment regarding potentiating negative effects produced by cooling meteorological factors. The assessment of developing general and local thermoregulation disorders revealed that certain individual peculiarities made a substantial contribution into their development. Among them, we can mention long-term outdoor work (60 % of work time or more) under exposure to cooling meteorological factors; a chronic pathology; tobacco smoking. The results produced by this study allowed us to suggest an integrated model for risk assessment, management and communication about health risks caused by working under exposure to cooling meteorological factors.

Efficient Bayes estimators of sensitive proportion with simple and mixture priors using direct and indirect responses

In this study, efficient Bayes estimators of sensitive proportion are proposed. It is documented that indirect reports increase variances of the estimates. To counteract this increase in variances we divided the total sample size, n = n 1+n 2, such that n 1 individuals record direct responses and n 2 individuals record indirect responses. The decision that a group of individuals should report indirect or direct responses would be based on distinct known factors. Bayes estimates and subsequent posterior risks are calculated taking into account different prior distributions, loss functions and a generalized randomized response technique. The impact of design parameters and the number of responses obtained using direct and indirect questioning techniques on the relative efficiencies are investigated. Graphical and numerical results indicate that the proposed estimators are better than the existing.

Bayesian Analysis of 3-Component Unit Lindley Mixture Model with Application to Extreme Observations

Bayesian inference of the 3-component unit Lindley right censored mixture is presented in this paper. The posterior distributions of the parameters are derived assuming informative (gamma) as well as noninformative (uniform and Jeffreys) priors. For the gamma (informative) prior, hyperparameters are elicited using prior predictive distribution. The Bayesian estimation has been carried out considering both symmetric and asymmetric loss functions (squared error, quadratic, weighted, and precautionary loss functions). Simulation studies for various sample sizes and different threshold values (test termination times) are considered to evaluate the performances of the Bayes estimators w.r.t their posterior risks under the said loss functions. Real life flood data from Naser Lake is also analyzed as a 3-component mixture for the sake of illustrative purpose. The simulation study and data analysis reveals that the estimates under informative prior perform better than the noninformative priors. Also, it is observed that the increase in sample size and the threshold value (test termination time) are inversely proportional to the posterior risks. Among the loss functions considered, the loss functions performance from the best to the least, w.r.t the posterior risk, is as follows: precautionary loss function &lt; weighted loss function &lt; quadratic loss function &lt; squared error loss function. Posterior risks are directly proportional to the sample size and threshold value (test termination time).