Bayesian Estimation Research Articles

Bayesian inference for reliability of K-out-of-N: G repairable retrial systems with mixed standbys, switching failure and reboot delay

Existing reliability studies on K-out-of-N: G repairable retrial systems with mixed standbys mainly consider the case where the standby switching is completely reliable and the repair time follows an exponential distribution, and most of them directly analyze the system reliability indices based on probability theory. Given the existence of such phenomenon as standby switching failure in engineering, this paper proposes a novel reliability model of K-out-of-N: G repairable retrial system with switching failure, and performs statistical inference on the reliability to realize the modeling and evaluation of the system. The considered system consists of mixed standbys and a repairer with vacation. When an operating component fails, the warm standby one is switched to the operating one immediately, and the probability of switching failure during the switchover process is p. In the case where the repair time of failed components follows a general distribution, based on the supplementary variable method and recursive algorithm, the steps for calculating the system steady-state availability are presented. In the case of unknown parameters for repair time and retrial time, the Bayesian estimator of the steady-state availability under the squared error loss function and highest posterior density (HPD) confidence interval are obtained. In numerical simulation, the system reliability inference is realized by using the Monte Carlo (MC) method, and the validity of the inference method is analyzed.

Analysis of Xgamma distribution using adaptive Type-I progressively censored competing risks data with applications

This paper considers the competing risks model with two causes of death to analyze time-to-event data for a group of male mice exposed to three hundred roentgen radiation for 5–6 weeks. The analysis is based on the assumption that the parent distribution is the Xgamma distribution and the data are gathered using an adaptive Type-I progressively censored sample. Two estimation approaches are considered to complete the analysis: maximum likelihood and Bayesian methods. Besides acquiring the estimations of the model parameters, the estimations of the reliability and failure rate are also discussed. Both point and interval estimates using both estimation approaches are studied. In Bayesian estimations, the squared error loss function is used and the Markov Chain Monte Carlo technique is proposed to get samples from the joint posterior distribution. The various methods are compared using simulation studies to compare their performance. The mentioned radiation data set is investigated and the analysis showed the suitability of the competing risks model with Xgamma distribution to analyze the data and to estimate the reliability metrics.

A note on Bayesian inference for the bivariate pseudo-exponential model

In this present work, we discuss the Bayesian inference for the Bivariate Pseudo-exponential distribution. Initially, we assume independent gamma priors and Pseudo-gamma priors for the Pseudo-exponential parameters. Possible conjugacy is investigated in both full and sub-models. In some special sub-cases, conjugate priors can be identified. We are primarily interested in deriving the posterior means for each prior assumed and comparing each of the posterior means with the maximum likelihood estimators. Finally, all the Bayesian analyses are illustrated with a simulation study to demonstrate the performance of Bayesian parameter estimates using a variety of informative and non-informative priors, also illustrated with real-life applications.

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

Optimal Inference of Hidden Markov Models Through Expert-Acquired Data.

This paper focuses on inferring a general class of hidden Markov models (HMMs) using data acquired from experts. Expert-acquired data contain decisions/actions made by humans/users for various objectives, such as navigation data reflecting drivers' behavior, cybersecurity data carrying defender decisions, and biological data containing the biologist's actions (e.g., interventions and experiments). Conventional inference methods rely on temporal changes in data without accounting for expert knowledge. This paper incorporates expert knowledge into the inference of HMMs by modeling expert behavior as an imperfect reinforcement learning agent. The proposed method optimally quantifies experts' perceptions about the system model, which, alongside the temporal changes in data, contributes to the inference process. The proposed inference method is derived through a combination of dynamic programming and optimal recursive Bayesian estimation. The applicability of this method is demonstrated to a wide range of inference criteria, such as maximum likelihood and maximum a posteriori. The performance of the proposed method is investigated through a comprehensive numerical experiment using a benchmark problem and biological networks.

State Policies Regulating Firearms and Changes in Firearm Mortality

Despite high social and public health costs of firearm violence in the United States, the effects of many policies designed to reduce firearm mortality remain uncertain. To estimate the individual and joint effect sizes of state firearm policies on firearm-related mortality. In this comparative effectiveness study, bayesian methods were used to model panel data of annual, state-level mortality rates (1979-2019) for all US firearm decedents, with analyses conducted in October 2023. Six classes of firearms policies: background checks, minimum age, waiting periods, child access, concealed carry, and stand-your-ground laws. Primary outcomes (total firearm deaths, firearm homicide deaths, and firearm suicide deaths) were assessed using the National Vital Statistics System. Bayesian estimation was used to estimate the partial association of changes in firearms policies with subsequent changes in firearm mortality. The estimated effect sizes of individual policies 5 or more years after implementation were generally small in magnitude and had considerable uncertainty. The policy class with the highest probability of reducing firearm deaths was child-access prevention laws, estimated to reduce overall firearm mortality by 6% (80% credible interval [CrI], -2% to -9%). The policy class with the highest probability of increasing firearm deaths was stand-your-ground laws, estimated to increase firearm homicides by 6% (80% CrI, 0% to 13% increase). Estimates of association of implementing multiple firearm restrictions with subsequent changes in firearm mortality yielded larger effect sizes. Moving from the most permissive to most restrictive set of firearm policies was associated with an estimated 20% reduction in firearm deaths (80% CrI, 10% to 28% reduction), with a 0.99 probability of any reductions in firearm death rates. In this comparative effectiveness study of state firearm policies, the joint effect estimates of combinations of firearm laws were calculated, showing that restrictive firearm policies were associated with substantial reductions in firearm mortality. Although policymakers would benefit from knowing the effects of individual policies, the estimated changes in firearm mortality following implementation of individual policies were often small and uncertain.

On the Association of GW190425 with Its Potential Electromagnetic Counterpart FRB 20190425A

Recent work by Moroianu et al. has suggested that the binary neutron star (BNS) merger GW190425 might have a potential fast radio burst (FRB) counterpart association, FRB20190425A, at the 2.8σ level of confidence with a likely host galaxy association, namely UGC10667. The authors argue that the observations are consistent with a long-lived hypermassive neutron star (HMNS) that formed promptly after the BNS merger and was stable for approximately 2.5 hr before promptly collapsing into a black hole. Recently, Bhardwaj et al. conclusively associated FRB20190425A with UGC10667, potentially providing a direct host galaxy candidate for GW190425. In this work, we examine the multimessenger association based on the spacetime localization overlaps between GW190425 and the FRB host galaxy UGC10667 and find that the odds for a coincident association are O(5) . We validate this estimate by using a Gaussian process density estimator. Assuming that the association is indeed real, we then perform Bayesian parameter estimation on GW190425 assuming that the BNS event took place in UGC10667. We find that the viewing angle of GW190425 excludes an on-axis system at p(θ v > 30°) ≈ 99.99%, highly favoring an off-axis system similar to GRB 170817A. We also find a slightly higher source frame total mass for the binary, namely, mtotal=3.42−0.11+0.34M⊙ , leading to an increase in the probability of prompt collapse into a black hole and therefore disfavors the long-lived HMNS formation scenario. Given our findings, we conclude that the association between GW190425 and FRB20190425A is disfavoured by current state-of-the-art gravitational-wave analyses.

Measurement and Uncertainty Preserving Parametric Modeling for Continuous Latent Variables With Discrete Indicators and External Variables

Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has received attention in models for continuous observable variables but to date has not been examined in the context of discrete variables. This work demonstrates that interpretational confounding can occur in models for discrete variables, and develops a multistage Bayesian estimation approach to deal with this problem. The key features of this approach are that it is (a) measurement preserving, in that it precludes the possibility of interpretational confounding, and (b) uncertainty preserving, in that the uncertainty from the earlier stage of estimating the measurement model is propagated to the second stage of estimating the relations between the latent variable(s) and any covariates or outcomes. Previous work on these methods had only considered models for continuous observed variables, and software was limited to models with a single latent variable and either covariates or outcomes. This work extends the approach and software to a more general class of solutions, including discrete variables, illustrating the procedures with analyses of real data. Functions for conducting the analyses in widely available software are provided.

On the Bayes risk of a sequential design for estimating a mean difference

On the Bayes risk of a sequential design for estimating a mean difference

Classical and Bayesian estimation of multicomponent stress–strength reliability with power Lindley distribution under progressive first-failure censored samples

This research article presents a methodology for estimating the multicomponent reliability based on progressively first-failure censored samples, where the underlying distribution of stress and strength is modelled using the power Lindley distribution. The classical and Bayesian estimation methods are utilized for estimating the multicomponent reliability. In the Bayesian estimation, the Markov Chain Monte Carlo approximation method is employed to obtain the posterior mean under a generalized entropy loss function. Various intervals including asymptotic confidence, bootstrap-p confidence, bootstrap-t confidence, Bayesian credible, and highest posterior density credible intervals are computed. A simulation study is conducted to evaluate the performance of the proposed methodology. Also, two different real data applications are presented to illustrate the practicality of the approach.

Statistical inference for marshall-olkin bivariate Kumaraswamy distribution under adaptive progressive hybrid censored dependent competing risks data

Abstract The statistical inference under competing risks model is of great significance in reliability analysis and it is more practical to assume that they have dependent competing causes of failure in actual situations. In this article, we make inference for unknown parameters of a Marshall-Olkin bivariate Kumaraswamy distribution under adaptive progressive hybrid censoring mechanism. The maximum likelihood estimations of the unknown parameters are derived, and the Fisher information matrix is then employed to construct asymptotic confidence intervals. Bayes estimates are evaluated against squared error and linex loss functions assuming ordered Gamma-Dirichlet and Gamma-Dirichlet prior distributions for order restriction and without order restriction cases respectively. The Metropolis-Hasting and Lindley techniques are applied to acquire the estimates of all unknown parameters. A thorough simulation analysis is demonstrated to assess the performance of the supplied approaches across various sample sizes. The usefulness of the techniques is illustrated using real engineering data to prove their versatility in practical applications.

Optimizing Genomic Parental Selection for Categorical and Continuous-Categorical Multi-Trait Mixtures.

This study presents a novel approach for the optimization of genomic parental selection in breeding programs involving categorical and continuous-categorical multi-trait mixtures (CMs and CCMMs). Utilizing the Bayesian decision theory (BDT) and latent trait models within a multivariate normal distribution framework, we address the complexities of selecting new parental lines across ordinal and continuous traits for breeding. Our methodology enhances precision and flexibility in genetic selection, validated through extensive simulations. This unified approach presents significant potential for the advancement of genetic improvements in diverse breeding contexts, underscoring the importance of integrating both categorical and continuous traits in genomic selection frameworks.

From pre-test and post-test probabilities to medical decision making

BackgroundA central goal of modern evidence-based medicine is the development of simple and easy to use tools that help clinicians integrate quantitative information into medical decision-making. The Bayesian Pre-test/Post-test Probability (BPP) framework is arguably the most well known of such tools and provides a formal approach to quantify diagnostic uncertainty given the result of a medical test or the presence of a clinical sign. Yet, clinical decision-making goes beyond quantifying diagnostic uncertainty and requires that that uncertainty be balanced against the various costs and benefits associated with each possible decision. Despite increasing attention in recent years, simple and flexible approaches to quantitative clinical decision-making have remained elusive.MethodsWe extend the BPP framework using concepts of Bayesian Decision Theory. By integrating cost, we can expand the BPP framework to allow for clinical decision-making.ResultsWe develop a simple quantitative framework for binary clinical decisions (e.g., action/inaction, treat/no-treat, test/no-test). Let p be the pre-test or post-test probability that a patient has disease. We show that r∗=(1-p)/p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{*}=(1-p)/p$$\\end{document} represents a critical value called a decision boundary. In terms of the relative cost of under- to over-acting, r∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{*}$$\\end{document} represents the critical value at which action and inaction are equally optimal. We demonstrate how this decision boundary can be used at the bedside through case studies and as a research tool through a reanalysis of a recent study which found widespread misestimation of pre-test and post-test probabilities among clinicians.ConclusionsOur approach is so simple that it should be thought of as a core, yet previously overlooked, part of the BPP framework. Unlike prior approaches to quantitative clinical decision-making, our approach requires little more than a hand-held calculator, is applicable in almost any setting where the BPP framework can be used, and excels in situations where the costs and benefits associated with a particular decision are patient-specific and difficult to quantify.

Support for the Time-Varying Drift Rate Model of Perceptual Discrimination in Dynamic and Static Noise Using Bayesian Model-Fitting Methodology.

The drift-diffusion model (DDM) is a common approach to understanding human decision making. It considers decision making as accumulation of evidence about visual stimuli until sufficient evidence is reached to make a decision (decision boundary). Recently, Smith and colleagues proposed an extension of DDM, the time-varying DDM (TV-DDM). Here, the standard simplification that evidence accumulation operates on a fully formed representation of perceptual information is replaced with a perceptual integration stage modulating evidence accumulation. They suggested that this model particularly captures decision making regarding stimuli with dynamic noise. We tested this new model in two studies by using Bayesian parameter estimation and model comparison with marginal likelihoods. The first study replicated Smith and colleagues' findings by utilizing the classical random-dot kinomatogram (RDK) task, which requires judging the motion direction of randomly moving dots (motion discrimination task). In the second study, we used a novel type of stimulus designed to be like RDKs but with randomized hue of stationary dots (color discrimination task). This study also found TV-DDM to be superior, suggesting that perceptual integration is also relevant for static noise possibly where integration over space is required. We also found support for within-trial changes in decision boundaries ("collapsing boundaries"). Interestingly, and in contrast to most studies, the boundaries increased with increasing task difficulty (amount of noise). Future studies will need to test this finding in a formal model.

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Partial Bayes Estimation in Two-Parameter Rayleigh Distribution

In Bayesian paradigm, when we have no proper information regarding the joint parameters of the model of the variable and the aim is to estimate only one of them in presence of another nuisance parameter, we introduce an estimation approach known as ‘Partial Bayes estimation’. Here, two-parameter Rayleigh distribution is considered with location parameter μ and scale parameter λ and both are unknown. Partial Bayes estimates of the parameter of interest λ are derived both under non-informative uniform prior and informative gamma prior by plugging the estimate of another parameter μ , obtained by some other classical method using ordered samples. As, the maximum likelihood estimate of the parameters cannot be obtained explicitly, we also propose an estimation method closed to maximum likelihood estimate using the ordered samples. We use Kullback-Leibler distance loss derived using two Rayleigh density functions, precautionary loss and weighted squared error loss functions to compute the risk values. Simulation studies are performed to assess the performance of the Partial Bayes estimates through integrated risks under different loss functions. Two real datasets are used to show the applicability of the proposed Partial Bayes estimation technique.

Analysis of the lifetime performance index in Gompertz distribution based on k-record values

The lifetime performance index plays a crucial role in manufacturing procedures as it provides valuable insights into the overall quality of a product. Considering the Gompertz distribution as a widely applicable statistical distribution, this index to emphasize the effect in analyzing lifetime data. This paper investigates the inference techniques associated with the lifetime performance index for the Gompertz distribution when k-record values are available. For this problem, two innovative methods are introduced utilizing the concept of the generalized pivotal variable. These methods are not only applicable to hypothesis tests but also enable the construction of confidence intervals. To further enhance the accuracy of estimation, the study proposes Bayesian estimation techniques based on the Metropolis–Hastings algorithms. To assess the efficacy of these methods, a simulation study is conducted. The results demonstrate that all three procedures exhibit exceptional performance, even when confronted with datasets consisting of small k-record values. Moreover, a dataset is utilized to demonstrate the implementation of these three methods.

Bayesian estimation of the prevalence of antimicrobial resistance: a mathematical modelling study.

Estimates of the prevalence of antimicrobial resistance (AMR) underpin effective antimicrobial stewardship, infection prevention and control, and optimal deployment of antimicrobial agents. Typically, the prevalence of AMR is determined from real-world antimicrobial susceptibility data that are time delimited, sparse, and often biased, potentially resulting in harmful and wasteful decision-making. Frequentist methods are resource intensive because they rely on large datasets. To determine whether a Bayesian approach could present a more reliable and more resource-efficient way to estimate population prevalence of AMR than traditional frequentist methods. Retrospectively collected, open-source, real-world pseudonymized healthcare data were used to develop a Bayesian approach for estimating the prevalence of AMR by combination with prior AMR information from a contextualized review of literature. Iterative random sampling and cross-validation were used to assess the predictive accuracy and potential resource efficiency of the Bayesian approach compared with a standard frequentist approach. Bayesian estimation of AMR prevalence made fewer extreme estimation errors than a frequentist estimation approach [n = 74 (6.4%) versus n = 136 (11.8%)] and required fewer observed antimicrobial susceptibility results per pathogen on average [mean = 28.8 (SD = 22.1) versus mean = 34.4 (SD = 30.1)] to avoid any extreme estimation errors in 50 iterations of the cross-validation. The Bayesian approach was maximally effective and efficient for drug-pathogen combinations where the actual prevalence of resistance was not close to 0% or 100%. Bayesian estimation of the prevalence of AMR could provide a simple, resource-efficient approach to better inform population infection management where uncertainty about AMR prevalence is high.

Accounting for ground-motion uncertainty in empirical seismic fragility modeling

Seismic fragility models provide a probabilistic relation between ground-motion intensity and damage, making them a crucial component of many regional risk assessments. Estimating such models from damage data gathered after past earthquakes is challenging because of uncertainty in the ground-motion intensity the structures were subjected to. Here, we develop a Bayesian estimation procedure that performs joint inference over ground-motion intensity and fragility model parameters. When applied to simulated damage data, the proposed method can recover the data-generating fragility functions, while the traditionally used method, employing fixed, best-estimate, intensity values, fails to do so. Analyses using synthetic data with known properties show that the traditional method results in flatter fragility functions that overestimate damage probabilities for low-intensity values and underestimate probabilities for large values. Similar trends are observed when comparing both methods on real damage data. The results suggest that neglecting ground-motion uncertainty manifests in apparent dispersion in the estimated fragility functions. This undesirable feature can be mitigated through the proposed Bayesian procedure.

Classical and Bayesian estimations of performance measures in G e o / G e o / 1 queue

. In this article, we consider an early arrival G e o / G e o / 1 queue from the statistical perspective. The estimations of parameters and system performances under Classical and Bayesian frameworks are considered. Based on queue length data, we attempt to study the uniform minimum-variance unbiased estimators (UMVUEs) and the closed Bayesian estimators for various queueing characteristics. We compare their properties using Monte Carlo (MC) simulations. As a comparison and improvement, based on arrival and departure data over a period, we use a Bivariate Beta distribution as joint prior, and solve the performance estimators using the properties of Gaussian hypergeometric function. We derive Bayesian estimators and conduct numerical simulations using Markov Chain Monte Carlo (MCMC) method.