Search Results (350)

Bayesian estimation of nonlinear mixed-effects models typically relies on Markov-Chain Monte Carlo (MCMC) methods due to the intractability of the posterior distribution. While widely used for longitudinal data with missing observations, the performance of MCMC algorithms is often taken for granted, despite their critical impact on inference quality. This paper investigates MCMC-based estimation for Bayesian nonlinear mixed-effects models with missing data, focusing on convergence behavior and computational efficiency. We propose a hybrid sampling framework that combines Gibbs sampling with Metropolis–Hastings (MH) and adaptive MH algorithms to improve mixing and stability. Convergence diagnostics, the effective sample size, and computational performance are systematically evaluated. Simulation studies assess the effects of the iteration length, burn-in proportion, and sample size, and the methodology is illustrated using orthodontic growth data and the Treatment of Lead-Exposed Children (TLC) trial. Full article

Component outage records in power systems are often limited, which makes it difficult to represent failure probabilities with deterministic point estimates. To address this issue, this paper proposes a reliability assessment framework that combines an improved Imprecise Dirichlet Model (IDM) with improved Transitional Markov Chain Monte Carlo (iTMCMC). The improved IDM introduces a sample-size-dependent hyperparameter to construct adaptive outage-probability intervals for different equipment categories. These interval probabilities are then propagated through iTMCMC to obtain interval-valued system reliability indices. In the sampling process, a reliability-oriented likelihood function is used to guide system-state exploration, and self-normalized weights are applied to maintain estimator consistency. A case study is conducted on a standard IEEE reliability test system. The results show that the improved IDM can provide adaptive component outage-probability intervals, while iTMCMC achieves more stable LOLP and EENS estimates than MC and MCMC. The interval propagation results further demonstrate that the proposed framework can transfer component-level probability uncertainty into system-level reliability-index intervals. The proposed method provides a practical tool for reliability assessment when component failure records are incomplete or insufficient. Full article

A Bayesian risk analysis technique based on power Ailamujia (PA) distribution has been developed in this work, which helps in identifying various types of risk factors with their specific utility. Prior distributions have been used in the models while Bayesian estimations have been done with the help of the use of standard squared error loss functions, such as the mean square error function together with a quadratic loss function. Analysis is then performed with the help of Markov chain Monte Carlo (MCMC) approaches and time and sensitivity analyses can be done precisely in the process. For practical demonstration of this technique, real-life data are analyzed and a comparison of our proposed technique is made with the classical method of prediction. Also, we apply the proposed methodology to two distinct real-world datasets: the biomedical AIDSSI dataset from the Amsterdam Cohort Studies on HIV infection, and a sports dataset comprising UEFA Champion’s League goal-scoring times. Crucially, we present a comprehensive goodness-of-fit analysis for both datasets to validate the suitability of the PA distribution before conducting the competing risks analysis. Full article

Robust variable selection methods have emerged as powerful tools for dissecting high-dimensional gene–environment interactions in longitudinal studies, owing to their ability to accommodate intra-cluster correlations, capture structured sparsity, and handle heavy-tailed repeated measures. Despite these advantages, variable selection-based interaction analysis still suffers from a lack of valid inferential tools to quantify the uncertainty associated with important gene–environment interactions. In this paper, we introduce the R package mixedBayes (version 0.2.5), which implements fully Bayesian robust mixed-effects models proposed in recent work for high-dimensional longitudinal gene–environment interaction analysis. Specifically, the package considers two major classes of mixed models. The first accommodates interactions between omics features and treatment effects arising from repeated-measures one-way ANOVA with high-dimensional genetic factors. The second provides a more general framework for modeling interactions between individual genetic main effects and environmental factors. Both models enable posterior Bayesian inference via Markov chain Monte Carlo (MCMC). We provide detailed numerical examples and accompanying R code to facilitate robust interaction analysis using mixedBayes. In addition, a case study based on longitudinal asthma data with high-dimensional SNP measurements is presented. Full article

This paper addresses the estimation of the multi-component stress–strength reliability when both the strength variables and the stress variable follow the one-parameter Garhy distribution. Data are assumed to arise from a unified hybrid censoring scheme, which generalizes both Type-I and Type-II hybrid censoring. A closed-form expression for the reliability parameter $R_{m,k}=P(\mathrm{at}\mathrm{least}m\mathrm{of}(X_1,\dots ,X_k)>Y)$ is derived, enabling efficient computation. Three estimation procedures are developed: maximum likelihood estimation (MLE), Bayesian inference using Markov chain Monte Carlo (MCMC) with non-informative priors, and the Tierney–Kadane Laplace-type approximation for posterior moments. For each method, we provide complete mathematical derivations, including the likelihood function under unified hybrid censoring, the posterior conditionals, and the asymptotic distribution of the reliability via the Delta method. Furthermore, Bayesian estimation is extended to asymmetric loss functions, and posterior propriety is formally proven. To check the suitability of the proposed methods, a real data application on generator failure times in power systems is presented. Full article

Traditional maritime vessel tracking methods based on multi-static passive radar stations typically process all available observations, leading to substantial computational overhead and estimation variance. Furthermore, discrepancies in refresh rates and noise levels among stations often cause significant jumps in estimated positions between updates, resulting in trajectory discontinuities. To mitigate these issues, this paper introduces a multi-station cooperative vessel tracking framework based on a motion-constrained resample–move particle filter (MC-RMPF). In the proposed method, systematic resampling is first used to alleviate particle degeneracy, and a markov chain monte carlo (MCMC) move step is subsequently applied to rejuvenate the resampled particles under vessel-motion feasibility constraints. Additionally, a distributed detection network is constructed using directional data from multiple stations, dynamically selecting optimal observation subsets to balance localization accuracy with computational load. The experimental results demonstrate that, compared to the baseline methods, our method reduces the Root Mean Square Error and Circular Error Probability of position tracking by 23.5% and 21.7%, respectively. It exhibits strong reliability in challenging scenarios such as target maneuvers and temporary observation loss. Full article

This paper investigates the stress–strength reliability parameter $R=P(Y<X)$ for the Garhy distribution under upper-, lower-, and mixed-record schemes. The Garhy distribution, a flexible one-parameter lifetime model, is shown to provide an excellent fit to precipitation and medical (kidney dialysis) data, with Kolmogorov–Smirnov p-values of 0.9904 and 0.9072, respectively. Maximum likelihood estimators (MLEs) of R are developed, alongside Bayesian estimators using Jeffreys and extended Jeffreys priors under squared error loss. Markov chain Monte Carlo (MCMC) methods are employed for posterior inference. An extensive Monte Carlo simulation study reveals that: (i) MLEs converge under all record schemes but exhibit larger bias and lower efficiency compared to Bayesian estimators; (ii) Bayesian estimators, in contrast, demonstrate superior stability, lower mean squared error, and better bias control, especially for pure upper and lower records; (iii) mixed records consistently yield the most balanced and reliable estimates, capturing distributional information more effectively than single-type records; and (iv) the extended Jeffreys prior provides effective bias correction, outperforming the standard Jeffreys prior in many scenarios. Analysis of real-world datasets confirms the simulation findings, with Bayesian estimators under mixed records producing stable and accurate reliability estimates, outperforming MLE in terms of precision and stability. The results strongly advocate for Bayesian methodology with non-informative priors when assessing stress–strength reliability from record-breaking data. Full article

In this presented work, we execute a statistical data analysis on the viscous models of non-perfect fluid with a viscosity profile $\xi ={\xi }_0+({\xi }_1-{\xi }_{2}q)H$ as well as by taking an equation of state (EOS) characterized by inhomogeneity $p=\omega \rho +\mathsf{\Lambda }\left(t\right)$ and $\omega =\alpha -1$, in the absence of any non-canonical dark energy term with different observational datasets. For the validation of the theoretical study, we carry out Monte Carlo Markov Chain (MCMC) analysis using recent Hubble $H\left(z\right)$, DESI BAO and the Pantheon Plus (PP) datasets to derive the values of constraints. The best-fit results exhibit robust cross-dataset agreement and remain in full agreement with the parameters inferred within the $\mathsf{\Lambda }CDM$ model. Full article

This paper investigates the estimation of the stress–strength reliability parameter $R=P(Y<X)$ when both stress and strength follow independent Garhy distributions under progressive Type-II censoring schemes. A closed-form expression for $\mathit{R}$ is explicitly derived, enabling effective and precise calculation without numerical integration. The Garhy distribution, a flexible one-parameter lifetime model with an increasing hazard function, is confirmed by full-scale goodness-of-fit diagnostics. A Bayesian estimation model is trained on non-informative priors (normal and extended Jeffreys priors) under squared error loss. The posterior expectations are analytically intractable; we adopt two complementary methods of computation: (i) Markov Chain Monte Carlo (MCMC) using the Metropolis–Hastings algorithm and (ii) the Tierney–Kadane (TK) approximation, which provides extremely precise analytical estimates with significantly reduced computational burden. Monte Carlo simulations are large-scale and compare the proposed estimators under different censoring schemes, sample sizes, and parameter configurations in terms of bias and mean squared error (MSE). The methodology is further applied to a real medical dataset comprising kidney dialysis patient survival times, demonstrating its practical relevance in clinical reliability assessment. Results consistently indicate that Bayesian methods, particularly with the extended Jeffreys prior, outperform classical MLEs in terms of stability and accuracy, especially under heavy censoring. Moreover, the TK approximation yields estimates virtually identical to MCMC while requiring only a fraction of the computational effort. We further extend the TK framework to approximate the posterior variance of R and the expected log-likelihood, providing a fully analytical alternative to MCMC for comprehensive Bayesian inference. Full article

To address the challenges of difficult value quantification, lack of market benchmarks, and scarcity of historical data for embedded software amidst the intelligent transformation of equipment systems, this study develops a scientific price estimation method based on functional capability contribution. A nonlinear pricing model is constructed to accurately characterize the two-stage evolution of software price: diminishing marginal utility during the mature technology accumulation stage and exponential growth during the technical bottleneck breakthrough stage. To ensure the consistency of pricing logic between hardware and software, a penalty function is innovatively designed to modify the standard likelihood function, effectively transforming practical business logic into a model regularization term. Parameter estimation is achieved by employing a Bayesian inference framework integrated with operational constraints, utilizing Markov Chain Monte Carlo (MCMC) sampling to realize robust posterior inference under small-sample constraints. Empirical analysis demonstrates that the proposed method achieves superior cross-domain data transfer performance compared to traditional baseline models, with a Leave-One-Out Cross-Validation (LOOCV) Mean Absolute Percentage Error (MAPE) of 21.2%. This research provides a practical value-oriented price estimation method for embedded equipment software pricing. Full article

This study develops confidence and credible intervals for the variance of the zero-inflated two-parameter Rayleigh distribution, a flexible model for non-negative data with excess zeros. Seven approaches are proposed: Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), the standard confidence interval, the approximation normal, the percentile bootstrap, the bootstrap method with standard error, and the generalized confidence interval (GCI). Their performance is assessed through Monte Carlo simulation using coverage probability (CP) and expected length (EL). The results show that the Bayesian HPD interval performs best overall, attaining coverage close to the nominal level while yielding shorter intervals than the alternatives, especially for small samples. The methods are illustrated with road traffic fatality data from Chiang Mai Province, Thailand, recorded in March 2024. These findings support the practical usefulness of the HPD approach for variance interval estimation in zero-inflated continuous models. Full article

The zero-inflated two-parameter Rayleigh (ZITR) distribution provides a flexible framework for modeling data with excess zeros and positive observations following a two-parameter Rayleigh distribution. It is particularly suitable for right-skewed data and has applications in areas such as road traffic mortality and survival analysis. This study develops and compares several methods for constructing confidence intervals for the difference and ratio of variances from two independent ZITR populations. The considered methods include Bayesian approaches based on Markov Chain Monte Carlo (MCMC) and highest posterior density (HPD) intervals, as well as the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), approximate normal (AN), percentile bootstrap (PB), and bootstrap with standard error (BS). The performance of these methods is evaluated via Monte Carlo simulations under various parameter settings and sample sizes, using coverage probability and expected interval length as performance criteria. The results indicate that the Bayesian HPD method generally performs well across a wide range of scenarios. A real-data application using road traffic mortality data from January 2025 in Chanthaburi and Narathiwat provinces is also presented, demonstrating the practical usefulness of the proposed approaches for comparing the variance structure between the two regions. Full article

The evolution of the deceleration parameter $q\left(z\right)$ plays a crucial role in understanding the dynamics of dark energy within the framework of modern cosmology. In this study, we perform a parametric reconstruction of $q\left(z\right)$ in a spatially flat Friedmann–Robertson–Walker (FLRW) Universe composed of radiation, pressureless dark matter, and dark energy. We consider a physically motivated form of $q\left(z\right)$ that effectively describes the transition of the Universe from a decelerating to an accelerating expansion phase. This parametrization is incorporated into the Friedmann equations to derive the corresponding Hubble parameter, which is then confronted with a comprehensive set of observational data, including Hubble parameter measurements $H\left(z\right)$, Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) data. Employing the Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters using the combined $H\left(z\right)+SNIa+BAO$ dataset. The best-fit parameters are subsequently used to reconstruct the cosmographic quantities, such as the deceleration, jerk, and snap parameters, which provide deeper insight into the expansion history of the Universe. Finally, a comparative analysis with the standard $\Lambda$CDM model is carried out to assess the compatibility and effectiveness of the proposed parametrization. Full article

This paper investigates the prediction of unobserved future failure times for the heavy-tailed Log-Logistic distribution under Progressive Type-II censoring. We first develop point and interval estimates for the unknown parameters using both frequentist maximum likelihood and Bayesian approaches. For predicting future failures, we derive three distinct point predictors: the Best Unbiased Predictor (BUP), the Conditional Median Predictor (CMP), and the Bayesian Predictor (BP). Corresponding prediction intervals are constructed using frequentist pivotal quantities, Bayesian Equal-Tailed Intervals (ETIs), and Highest Posterior Density (HPD) methods. The Bayesian procedures are implemented via Markov chain Monte Carlo (MCMC) sampling. We evaluate the finite-sample performance of the proposed methodologies through a Monte Carlo simulation study and further validate them using two real-world datasets, namely bladder cancer remission times and guinea pig survival times. The numerical results indicate that the proposed BP, particularly under the empirical prior, provides the most accurate and stable overall performance for point prediction, while the frequentist predictors become less reliable in extreme heavy-tailed settings. For interval prediction, the Bayesian HPD method consistently outperforms the alternatives, substantially reducing interval lengths for right-skewed data while maintaining the nominal coverage probability. Full article

A novel flexible single-parameter polynomial distribution is presented in this study. The forms of hazard rate and density functions are examined. Additionally, exact formulas for a number of numerical characteristics of distributions are obtained. Stochastic ordering, the moment technique, the maximum likelihood, and a Bayesian analysis of this novel distribution based on type II censored data are used to derive the extreme order statistics. We construct Bayes estimators and the associated posterior risks using a variety of loss functions, such as the generalized quadratic, entropy, and Linex functions. Since tractable analytical formulations of these estimators are unattainable, we suggest using a simulation technique based on Markov chain Monte-Carlo (MCMC) to examine their performance. Furthermore, we construct maximum likelihood estimators given initial values for the model’s parameters. Additionally, we use integrated mean square error and Pitman’s proximity criteria to compare their performance with that of the Bayesian estimators. Lastly, we apply the new family to many real-world datasets to show its versatility, and we model cancer survival data using this new distribution to explain our methodology. Full article