Response surface methodology has been known to be an effective tool for improving an overall manufacturing process where quality requirements are fulfilled. This work proposes a double-robust Bayesian modeling method that can simultaneously cope with variable selection, model form uncertainty, and nonnormality for quality prediction. Double robustness is achieved by specifying the class of spherically symmetric distributions for the errors and accounting for model form uncertainty through Bayesian model averaging. Furthermore, with a special choice in the subharmonic priors for the regression coefficients, a closed-form expression of the marginal posterior distribution of each candidate model is obtained, which is not only free of the error distributions (other than spherical symmetry) but also can be easily computed using standard software. To provide a better interpretation of the model, a special prior is specified for the model space to maintain and reflect the hierarchical or structural relationships among input variables. The proposed Bayesian method has the properties of variable selection consistency and prediction consistency under Bayesian model averaging. Through numerical experiments and a case study, the proposed double-robust Bayesian modeling method is shown to achieve results superior to those of the existing established methods in prediction and variable selection in linear models under different types of error distributions.

The dynamic modulus of asphalt mixtures is a key design parameter in pavement design, which significantly impacts the mechanical properties of asphalt pavements. This study simulated dynamic modulus tests of asphalt mixtures using the three-dimensional (3D) discrete element method (DEM) to investigate mechanical behaviors such as the loading-bearing ratio of individual aggregates. Fine-grained AC-13 and medium-grained AC-20 asphalt mixture models were randomly constructed in the DEM program using user-defined methods. The dynamic modulus and phase angle values of the asphalt mixtures were predicted. By comparing laboratory experiments with DEM simulation results, the model was validated, and the effects of temperature and loading frequency on the dynamic modulus were explored. Further exploration was conducted on the loading-bearing ratio and mechanical interactions among aggregates of different sizes within the mixtures. The results show that the 3D DEM model can accurately predict the dynamic modulus and phase angle of asphalt mixtures. Temperature and frequency have an impact on these parameters, and the increase in gradation has an impact on the loading-bearing ratio, due to the proportion of coarse aggregates.

Accurate prediction of cobalt ion concentration is important for maintaining electrolyte purity and process stability in zinc hydrometallurgical purification. However, conventional laboratory analysis is time-consuming and difficult to support timely process adjustment. This work proposes a GWO-VMD-TCN-GRU framework for one-step-ahead prediction of cobalt ion concentration in the second-stage purification process. GWO is used to optimize VMD parameters and decompose the non-stationary concentration series into trend and detail components, while the TCN-GRU network captures local fluctuations and temporal dependencies. Experiments were conducted using 720 hourly samples collected over 30 consecutive days. The final selected model, evaluated on the fixed chronological test set, achieved RMSE, MAE, R², and KGE values of 0.1349, 0.1095, 0.9922, and 0.9710, respectively. Compared with representative statistical, machine learning, and deep learning baseline models evaluated under the same fixed chronological testing protocol, the proposed GWO-VMD-TCN-GRU model reduced RMSE by 75.3% to 94.5% and MAE by 73.1% to 94.3%. Five-fold time-series validation was further conducted to evaluate temporal generalization across chronological folds, with average R2 and KGE values of 0.9824 and 0.9582, respectively. A SHAP-based interpretability analysis showed that lagged trend features contributed most to the prediction, while detail features provided supplementary information for short-term fluctuation tracking. Finally, a prototype software platform was developed to integrate offline model development, online prediction, three-stage purification visualization, zinc powder dosage recording, alarm information, and monitoring record export. Overall, the proposed framework demonstrates reliable short-term forecasting performance for cobalt ion concentration and provides predictive and early-warning information for purification monitoring and operator assessment of zinc powder addition.

Evaporators are key heat exchange components in organic Rankine cycle (ORC) systems for medium- and low-temperature waste heat recovery. Accurate prediction of the volumetric heat transfer coefficient (VHTC) is crucial for system design and operation. However, existing prediction approaches lack multidimensional feature representation, physical constraints, and interpretability, limiting their reliability and transparency in industrial applications. This work integrates multi-scale physical mechanisms with data-driven modeling to address the above limitations. After three-stage data preprocessing, the key modeling and interpretation method involves three core steps. First, a multi-scale physical feature fusion (MSPFF) system is constructed, covering microscopic fluid properties, mesoscopic flow-heat transfer states, and macroscopic system performance. Second, a physically-constrained deep neural network (PDNN) is designed, in which data-driven prediction is coupled with explicit physical constraints derived from heat transfer and energy conservation principles. Third, SHAP-based interpretability analysis is introduced to quantify feature contributions and reveal the dominant physical drivers of VHTC prediction. Experimental results show strong performance of the proposed model on the test set, with an R2 of 0.9568, an MAE of 0.0202 W/(m3·K), an MSE of 0.0007 (W/(m3·K))2, and an RMSE of 0.0260 W/(m3·K). The model also improved post-prediction physical consistency, with only 1.5% of the predicted samples showing physically contradictory trends and 3.1% exceeding the 10% energy-balance deviation criterion used for prediction-consistency evaluation. This work provides a high-precision, physically interpretable VHTC prediction tool for ORC evaporator optimization. It also provides a methodological reference for mechanism-data integrated modeling of complex heat transfer processes in waste heat utilization.

Global carbon neutrality targets and rapid digitalization are reshaping steel production, accelerating a transition toward low-carbon and data-driven operations. Artificial intelligence provides a pathway beyond experience-based practice and purely mechanistic metallurgy by leveraging large, heterogeneous industrial datasets. This work synthesizes applications across the steelmaking production chain, with emphasis on sensing and soft sensing, process modeling, and process optimization and control. It further aligns these methods with decarbonization pathways, including energy and process efficiency, feedstock and energy substitution such as hydrogen-assisted routes and scrap-based electric arc furnace production, and carbon capture, utilization, and storage. Evidence from research and industrial practice suggests improvements in product quality and yield, alongside reductions in energy intensity and emissions. Future progress will depend on stronger data infrastructure and governance, effective translation from research to plant deployment, and robust physics-informed and hybrid modeling to support generalization across processes and operating regimes.

For the first time, the theories and methods of subsampling techniques for joint mean and variance models are studied in the multi-source heterogeneous big data. Additionally, simulations are conducted to evaluate the significant effectiveness of the proposed method. With the rapid advancement of information technology, the generation and accumulation of multi-source big data have created rich resources for data analysis and decision-making. However, processing and analyzing large-scale data from diverse sources presents significant challenges for traditional statistical methods, including insufficient computational resources, transmission delays, and privacy concerns. As joint modeling of mean and variance is fundamental to statistical analysis and significantly impacts the accuracy and effectiveness of data interpretation, efficiently applying optimal subsampling techniques to massive joint mean and variance models in a distributed environment has become a critical issue in modern data analysis. In this paper, we propose a distributed subsampling algorithm based on joint mean and variance models to effectively address the subsample selection problem in multi-source big data environments. First, the asymptotic properties of the subsample estimator are analyzed under the assumption of full data. Next, the optimal subsampling probabilities and allocated subsample sizes for the k-th sub-dataset are derived. Finally, a two-step, approximately optimal subsampling algorithm based on joint mean and variance models is introduced. The performance of the proposed method is evaluated through simulation studies and a real-world energy consumption data analysis.

Complex process parameters and limited accuracy of traditional models lead to difficulties in quality control and low optimization efficiency. Therefore, a high-quality prediction and optimization method for electrolytic copper refining process is proposed. By integrating electrochemical principles (i.e., Butler-Volmer equation), graph convolution network (GCN), complementary ensemble empirical mode decomposition (CEEMD), RRT-based optimizer (RRTO) and convolutional block attention module (CBAM), the framework accurately predicts electrolytic copper quality. Compared with traditional single-task model, MT-DeepChemNet-CEEMD-RRTO-CBAM framework shows significant advantages in predicting quality indexes of electrolytic copper. Specifically, the root mean square error is 0.72, which is 19% lower than the 0.89 of the traditional single-task models, the mechanism consistency index (MDCI) reaches 0.94, which is 15% higher than the 0.82 of the traditional single-task models. In addition, the number of parameters of the framework is only 1.20 M, which is 86% less than that of the traditional single-task model, and the training time is also shortened from 217.00 s to 35.00 s, which is 83.87% less than that of the traditional single-task model. Through multi-task learning, the framework can predict multiple quality indicators simultaneously, make full use of the inherent correlation between different quality indicators, improve data utilization efficiency and reduce overfitting risk. Therefore, this work constructs an integrated modeling framework that combines electrochemical mechanism and multi-task deep learning. A high-precision prediction approach based on decomposition-optimization-attention is proposed. The multi-index collaborative quality prediction and optimization method of electrolytic copper refining process is improved.

Statistical inference can be adversely impacted by abrupt changes or ‘change points’ in data series, such as those found in climate change analysis. Therefore, recognizing these change points is crucial to ensure accurate and reliable analysis. In this paper, we propose a novel Bayesian adaptive LASSO quantile regression (QR) model to robustly detect and locate change points in univariate data series exhibiting a simple linear trend. The model incorporates an asymmetric Laplace distribution (ALD) for the model error and independent Laplace priors on the regression coefficients. The paper presents an efficient Markov chain Monte Carlo (MCMC) sampling algorithm that takes advantage of the mixture representations of the ALD and Laplace distributions to draw samples from the joint posterior distribution of the unknown parameters. Numerical studies demonstrate that our approach delivers robust and accurate detection for multiple change points, as evidenced by high true detection rates and low false discovery rates in scenarios of varying sample sizes, error distributions, and change points’ locations and jump sizes. The effectiveness of the proposed methodology is showcased through carefully designed simulation studies and two real-data applications, where our results exhibit favorable comparisons to those of an existing frequentist procedure. Thus, our proposed method offers a comprehensive solution for accurate change point analysis, further improving the reliability and applications of QR-based change point detection processes.

Technological advancements have led to the exponential growth of data, and traditional statistical methods are no longer applicable for large-scale data. Subsampling and subdata selection emerged as essential strategies to address these challenges. In this paper, we prove that under random sampling, the information contained in a subdata is constrained by the size of the subdata. We then propose an information-based joint optimal subdata selection (IBJOSS) algorithm, based on the D-optimality criterion, within the framework of joint mean and variance models. This algorithm leverages the properties of the joint mean and variance models to select an informative subdata from large-scale data, thereby effectively reducing computational complexity and maintaining statistical inference accuracy. Finally, we validate the effectiveness of the proposed algorithm through simulation studies and a real data example.

Questionnaires are widely used in clinical research and mental health studies, but their responses are usually more subjective than clinical biomarkers. Researchers may use latent variable models such as the item response theory (IRT) model to characterize individual ability, but response instability and small sample sizes can lead to increased uncertainty in estimation. Historical data from similar questionnaires may help reduce variation, but they must be incorporated adaptively. The challenge is further compounded by the need to ensure computational efficiency in IRT models with a large number of parameters. In this work, we develop a Bayesian framework for adaptive borrowing in IRT models based on an approximated normalized power prior (NPP) that treats the borrowing weight as a random parameter. The proposed method makes NPP feasible for general IRT models and is coupled with a full Bayesian data augmentation strategy that enables joint estimation of ability and item parameters through an efficient Gibbs sampler. In simulations, the approach adaptively increases borrowing when historical and current data are compatible and automatically downweights conflicting information. Relative to analyzes without borrowing, the method reduces variance and mean squared error while maintaining coverage across a range of test lengths, item discrimination profiles, and historical-current concordance scenarios. We illustrate the method by integrating historical mental health surveys into current assessments, yielding more precise ability estimates with preserved calibration. An efficient implementation is provided in our updated package NPP available on the Comprehensive R Archive Network.

The increasing complexity of production processes and rapid developments in digital technology have fueled the adoption of metamodels in quality design. Kriging has emerged as one of the most popular emulation methods for both deterministic and stochastic simulations. Conventional Kriging models with predetermined mean functions, such as ordinary or universal Kriging, may exhibit subpar predictive performance when strong trends exist. This paper proposes a novel variable selection procedure for the mean function that ensures prediction accuracy while using only a limited number of variables to capture the potential existing trends in deterministic simulations. The proposed method integrates the benefits of Bayesian variable selection and frequentist statistical tests. Initially, a group of potential models is chosen to build the mean function, employing the Bayesian method with priors designed to guarantee sparsity. This results in a significant reduction in the number of models to be considered in the next stage. Subsequently, each candidate model undergoes rigorous frequentist tests to thoroughly assess its reliability and validity. Extensive simulation studies are conducted using the well-known Borehole function and a real-life case. The results demonstrate the superiority of the proposed method over several existing approaches, establishing its effectiveness in achieving robust parameter design.

High-dimensional data arising in genomics, econometrics, and clinical medicine often exhibit substantial heterogeneity across multiple sources. While existing methods address multi-source heterogeneity, they do not adequately accommodate the combined challenges of high dimensionality and between-source heterogeneity. To address this gap, we propose a scalable Bayesian framework for multi-source heterogeneous quantile regression with spike-and-slab priors for simultaneous parameter estimation and feature selection. To overcome computational challenges, we combine mean-field variational inference with Laplace approximation and introduce a novel low-rank variational correction strategy that substantially improves approximation accuracy and adaptability in high-dimensional heterogeneous settings. This low-rank correction effectively captures the underlying dependence structure, leading to more robust and efficient inference. For model assessment and diagnostic analysis, we further develop a Bayesian score test coupled with local influence analysis. Extensive simulation studies and an analysis of The Cancer Genome Atlas (TCGA) data from four cancer cohorts (ESCA, PAAD, PCPG, and READ) demonstrate the computational efficiency, scalability, and practical utility of the proposed method in high-dimensional heterogeneous applications. The proposed low-rank variational correction algorithms are implemented in the R package LRQVB, which is publicly available on CRAN.

Accurate prediction of convective heat transfer and pressure drop characteristics in Plate Heat Exchanger (PHE) is crucial for optimizing Organic Rankine Cycle (ORC) under off-design conditions. To resolve the physical inconsistency and data scarcity inherent in empirical correlations, this work introduces a thermodynamically consistent neural model, Thermodynamic Network for Geometric Optimization of Plate Heat Exchanger (PHEGNet), designed for multi-objective geometric optimization. The architecture embeds steady-flow energy conservation and phase equilibrium equations directly into the learning process, enforcing strict thermodynamic admissibility across the operational manifold. To ensure model robustness, Latin Hypercube Sampling (LHS) addresses data sparsity, while SHapley Additive Explanations (SHAP) quantify the sensitivities of critical geometric parameters, including the chevron angle and plate spacing, to reveal underlying thermo-hydraulic coupling mechanisms. Validation against independent experimental data from open literature indicates that the model achieves a mean absolute percentage error (MAPE) of 0.91%, with a coefficient of determination (R2) of 0.99 for fluid temperature predictions. These insights guide a Multi-Population Co-Evolutionary MultiObjective Optimization (MPCMO) strategy to resolve the trade-offs between thermal enhancement and hydraulic resistance. Results demonstrate that PHE-GNet achieves a 13.6% reduction in pressure drop and a 16.2% reduction in total annualized cost. Notably, the strategy maintains a 93% performance retention rate across diverse off-design trajectories, proving its superior reliability for complex heat-mass transfer processes in offdesign energy systems.

State-of-the-art techniques for pavement performance evaluation have attracted considerable attention in recent years. Artificial Neural Networks (ANNs) can simulate the human brain to discover hidden patterns within datasets, thereby enhancing the accuracy of performance evaluations in civil engineering. Routine backcalculation of layer properties from Falling Weight Deflectometer (FWD) deflection time histories provide critical information for asphalt pavement performance assessment. This study proposes a general framework that integrates the ANN with swarm optimization algorithms for asphalt pavement layer property backcalculation at the project level. The proposed procedure employed the spectral element method (SEM) to calculate the deflection time histories, explicitly accounting for the dynamic effect of FWD loading and the viscoelastic property of asphalt concrete (AC). The geometrical characteristic of the load time history and the load-deflection hysteresis curve were extracted to construct the training dataset for the ANN model. Three swarm optimization algorithms were utilized to determine the initial weights and biases of the ANN. Subsequently, the parameters of the Williams-Landel-Ferry (WLF) function were optimized using the field temperatures and the backcalculated layer property to characterize the temperature-dependent behaviour of AC. A well agreement between the backcalculated and measured deflection time histories, together with the consistency of the backcalculated layer properties within reasonable ranges, demonstrated the feasibility of the proposed procedure. In contrast to conventional backpropagation neural networks (BPNNs), whose built-in optimization schemes tend to become trapped in local optima and may yield unreasonable layer properties, swarm optimization algorithms expand the candidate solution space and facilitate global optimization. The standard deviation (STD) and coefficient of variation (COV) obtained from ANNs enhanced with swarm optimization are significantly lower than those from BPNNs; the maximum reduction in COV for ANN + HPO (Hunter–Prey optimization) relative to BPNN exceeds 50%. The ANN + MA (Mayfly Algorithm) and ANN + HPO exhibit superior performance and greater computational efficiency for layer property backcalculation compared with a conventional ANN model.

Abstract Background Women on probation (community supervision) report high rates of adverse childhood experiences (ACEs) and ongoing trauma, yet little research has examined how trauma across the life course relates to perinatal outcomes during community supervision. This study examined associations between lifetime trauma and perinatal violence, infant separation, and postpartum mood symptoms among women who experienced pregnancy, childbirth, and postpartum while on probation. Methods We conducted a cross-sectional secondary analysis from N = 60 women in South-Central Texas who had a pregnancy within the past five years while on community supervision. Trauma exposures included selected ACEs and adulthood/perinatal trauma (domestic, intimate partner, and sexual violence). Outcomes were perinatal violence, permanent infant removal after childbirth, and postpartum mood symptoms (PHQ-2/GAD-2). We used logistic regression to examine associations between trauma exposures and outcomes; given the ordinal structure of key trauma measures, we used Kendall’s tau to estimate correlations between cumulative ACEs/lifetime trauma and perinatal outcomes. Results Participants spent an average of 5 years (SD = 3) on community supervision, and most reported partner violence ( n = 52, 87%); no mental health care in the year prior to their last arrest ( n = 55, 92%); and possible major depressive disorder ( n = 20, 33%) and generalized anxiety disorder ( n = 34, 57%). ACE prevalence included caregiver incarceration ( n = 34, 56%), physical abuse ( n = 25, 42%), witnessing abuse ( n = 27, 45%), foster care ( n = 17, 8%), and childhood sexual abuse ( n = 29, 48%); 25% reported four ( n = 9, 16%) or five ( n = 6, 10%) ACEs. Cumulative ACE exposure was correlated with perinatal violence ( p = 0.03), and childhood forced sexual intercourse was associated with perinatal violence ( p = 0.04). Trauma in adulthood was associated with permanent infant removal ( p = 0.003). Sexual violence in adulthood was correlated with cumulative ACE exposure and postpartum mood symptoms ( p = 0.006). Conclusions Trauma across the life course is associated with perinatal violence, infant removal, and postpartum mood symptoms among women on community supervision. Trauma-informed, gender-responsive perinatal and community supervision interventions are needed to improve safety, mental health, and family stability. Trial registration NA

Fouling resistance is a key indicator of heat-transfer degradation, but continuous acquisition remains difficult under varying operating conditions. Accurate current-state estimation is challenged by strong nonlinearity, multiscale temporal behavior, measurement noise, and heterogeneity among independent runs. A convolutional neural network-long short-term memory-second-order autoregressive (CNN-LSTM-AR2) architecture is developed for measurement-assisted soft sensing to address these characteristics. The architecture combines convolutional extraction of local temporal variations, LSTM representation of longer-range accumulation behavior, and observed autoregressive inputs, Rft−1 and Rft−2, to encode explicit recent-state information. Run-aware preprocessing preserves temporal integrity by separating operational runs, interrupting sequences at invalid targets, and preventing cross-boundary leakage. Evaluation on 771 test sequences from independently held-out laboratory runs yields R2 = 0.9755, RMSE = 0.0090 m2·K·kW−1, and MAE = 0.0073 m2·K·kW−1. Benchmark comparison demonstrates higher accuracy than conventional machine-learning and sequence-model baselines under the defined protocol. Controlled ablation identifies AR2 as the largest performance contributor, with test R2 decreasing to 0.5711 after removal. Multi-seed testing confirms stable improvement, while Holm-adjusted p-values remain significant at 0.006. SHapley Additive exPlanations (SHAP) analysis identifies lagged resistance and surface temperature as major contributors, while operating-condition stratification reveals greater estimation difficulty within intermediate U and Ts ranges. Single-sample inference requires 150.04 ms, remaining compatible with the 10-min acquisition interval. The architecture provides accurate, interpretable, and computationally feasible measurement-assisted fouling-resistance estimation, while broader industrial applicability requires external validation.

Edge computing technology enables in situ diagnosis based on neural networks in ground-penetrating radar (GPR) detection. However, there is a contradiction between the limited resources of radar terminal and the high resource demands of the pavement distress detection model. This paper proposed a lightweight GPR detection model based on joint pruning to address this issue. First, the model uses YOLOv5s as the basic model and EfficientNet as the backbone feature extraction network in training, achieving structure compression of the feature extraction network. Next, the filter pruning via geometric median is used to further remove the redundant filters of each convolutional layer. In addition, considering the distress diversity and background complexity, attention mechanisms are incorporated to enhance the algorithm's robustness. A dataset of structural distresses, including loose, cracked, empty, and poor interlayer, was constructed and brought into the training. The results show improvements in both identification accuracy and detection speed, with the mean average precision (mAP) reaching 91.5% and giga floating-point operations per second (Gflops) decreasing by 21.74%. The proposed method can automatically and efficiently extract information from GPR images, thus providing technical support for the deployment of radar equipment on resource-limited edge devices.

Accurate prediction of cadmium ion concentration is crucial for maintaining product quality, process stability, and environmental compliance in the zinc hydrometallurgy purification process. Traditional laboratory methods, which are slow and noise-sensitive, limit timely monitoring of electrolyte conditions and operational adjustment in the purification process. This work proposes an integrated framework that combines deep learning and Singular Spectrum Analysis (SSA) for robust and accurate prediction of cadmium ion concentration. Specifically, SSA decomposes the original cadmium ion concentration series into low-frequency trends and high-frequency details, enhancing the signal-to-noise ratio and generating frequency-specific features. These components are then fed into a dual-channel model, where Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory (BiLSTM) networks jointly capture local patterns and temporal dependencies, while residual learning is introduced to further improve stability and prediction accuracy. Experiments were conducted on 720 hourly cadmium ion concentration samples collected over 30 consecutive days, with 30 independent repeated runs. The results demonstrate that the proposed model achieves high prediction accuracy, with Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) reduced by 73.5%-78.9% and 63.6%-71.9%, respectively, while the coefficient of determination (R2) and Kling-Gupta efficiency (KGE) improve by up to 227.1% and 122.9%. Moreover, the model shows strong robustness under noisy and fluctuating conditions. Based on these findings, a prototype software system was developed to support timely monitoring, zinc powder dosing decisions, and anomaly detection in zinc hydrometallurgy purification.

Abstract This article focuses on estimating the process capacity index (PCI), 𝒞 pc \mathcal{C}_{\rm pc} , where the underlying distribution is a power generalized Weibull distribution, using maximum likelihood and Bayesian techniques. The 𝒞 pc \mathcal{C}_{\rm pc} index may be used to both normal and non-normal quality attributes. This article aims to accomplish three things: Using the maximum likelihood approach, we first determine the estimator of the PCI 𝒞 pc \mathcal{C}_{\rm pc} . Secondly, the Metropolis-Hastings Algorithm is used to study Bayesian estimation under four loss functions (symmetric and asymmetric). Third, the index 𝒞 pc \mathcal{C}_{\rm pc} ’s 95 confidence intervals are built using Bayesian and four bootstrap techniques. The point estimates of 𝒞 pc \mathcal{C}_{\rm pc} have been evaluated using Monte Carlo simulation in terms of mean square errors (MSEs), four bootstrap methods, and highest posterior density (HPD) credible intervals in relation to their average width (AW) and coverage probabilities (CPs). Using two real data sets – one pertaining to the size of electrical connections and the other to the amount of protein (in g) for adult patients at the Hospital Carlos Van Buren in Valparaiso, Chile – a comparable analysis to that employed in the simulations is conducted in order to illustrate the effectiveness of the suggested methods.

Semiparametric mixed-effects double regression models have demonstrated satisfactory efficacy across diverse applications of longitudinal studies. However, the estimation of these models often relies on the assumptions of normally distributed errors and complete data with no missing values. Therefore, such restrictions may limit the practical usage of these models when analyzing longitudinal data that exhibit heavy-tailed behaviors and/or contain missing values. This paper introduces a Bayesian quantile regression-based semiparametric mixed-effects double regression model for examining longitudinal data with non-ignorable missing responses. Here, the quantile regression is used to address non-normality issues, and the missing mechanism is defined through a logistic regression model. Our proposed algorithm can concurrently model both the mean and variance of the mixed effects as functions of predictors while investigating the predictor effects at different quantiles of interest. Additionally, we utilize the Bayesian adaptive LASSO hierarchical model to devise an effective Metropolis-Hastings-within-Gibbs computation algorithm for both estimation and variable selection purposes. Finally, we conduct different simulation studies and a real-data example to demonstrate the successful implementation of our proposed Bayesian methodology.