Minimum Prediction Error Research Articles

The Effect of Stimulation Intensity, Sampling Frequency, and Sample Synchronization in TMS-EEG on the TMS Pulse Artifact Amplitude and Duration.

Transcranial magnetic stimulation (TMS) coupled with electroencephalography (EEG) possesses diagnostic and therapeutic benefits. However, TMS provokes a large pulse artifact that momentarily obscures the cortical response, presenting a significant challenge for EEG data interpretation. We examined how stimulation intensity (SI), EEG sampling frequency (Fs) and synchronization of stimulation with EEG sampling influence the amplitude and duration of the pulse artifact. In eight healthy subjects, single-pulse TMS was administered to the primary motor cortex, due to its well-documented responsiveness to TMS. We applied two different SIs (90% and 120% of resting motor threshold, representing the commonly used subthreshold and suprathreshold levels) and Fs (conventional 5 kHz and high frequency 20 kHz) both with TMS synchronized with the EEG sampling and the conventional non-synchronized setting. Aside from removal of the DC-offset and epoching, no preprocessing was performed to the data. Using a random forest regression model, we identified that Fs had the largest impact on both the amplitude and duration of the pulse artifact, with median variable importance values of 1.444 and 1.327, respectively, followed by SI (0.964 and 1.083) and sampling synchronization (0.223 and 0.248). This indicated that Fs and SI are crucial for minimizing prediction error and thus play a pivotal role in accurately characterizing the pulse artifact. The results of this study enable focusing some of the study design parameters to minimize TMS pulse artifact, which is essential for both enhancing the reliability of clinical TMS-EEG applications and improving the overall integrity and interpretability of TMS-EEG data.

When direction matters: Neural correlates of interlimb coordination of rhythm and beat

In a previous experiment, we found evidence for a bodily hierarchy governing interlimb coordination of rhythm and beat, using five effectors: 1) Left foot, 2) Right foot, 3) Left hand, 4) Right hand and 5) Voice. The hierarchy implies that, during simultaneous rhythm and beat performance and using combinations of two of these effectors, executing the task by performing the rhythm with an effector that has a higher number than the beat effector is significantly easier than vice versa. To investigate the neural underpinnings of this proposed bodily hierarchy, we here scanned 46 professional musicians using fMRI as they performed a rhythmic pattern with one effector while keeping the beat with another. The conditions combined the voice and the right hand (V + RH), the right hand and the left hand (RH + LH), and the left hand and the right foot (LH + RF). Each effector combination was performed with and against the bodily hierarchy. Going against the bodily hierarchy increased tapping errors significantly and also increased activity in key brain areas functionally associated with top-down sensorimotor control and bottom-up feedback processing, such as the cerebellum and SMA. Conversely, going with the bodily hierarchy engaged areas functionally associated with the default mode network and regions involved in emotion processing. Theories of general brain function that hold prediction as a key principle, propose that action and perception are governed by the brain's attempt to minimise prediction error at different levels in the brain. Following this viewpoint, our results indicate that going against the hierarchy induces stronger prediction errors, while going with the hierarchy allows for a higher degree of automatization. Our results also support the notion of a bodily hierarchy in motor control that prioritizes certain conductive and supportive tapping roles in specific effector combinations.

Parallelisms and deviations: two fundamentals of an aesthetics of poetic diction.

Poetic diction routinely involves two complementary classes of features: (i) parallelisms, i.e. repetitive patterns (rhyme, metre, alliteration, etc.) that enhance the predictability of upcoming words, and (ii) poetic deviations that challenge standard expectations/predictions regarding regular word form and order. The present study investigated how these two prediction-modulating fundamentals of poetic diction affect the cognitive processing and aesthetic evaluation of poems, humoristic couplets and proverbs. We developed quantitative measures of these two groups of text features. Across the three text genres, higher deviation scores reduced both comprehensibility and aesthetic liking whereas higher parallelism scores enhanced these. The positive effects of parallelism are significantly stronger than the concurrent negative effects of the features of deviation. These results are in accord with the hypothesis that art reception involves an interplay of prediction errors and prediction error minimization, with the latter paving the way for processing fluency and aesthetic liking. This article is part of the theme issue 'Art, aesthetics and predictive processing: theoretical and empirical perspectives'.

Being alive to the world: an artist's perspective on predictive processing.

I consider predictive processing (PP) from the perspective of an artist who also conducts scientific research into art and perception. This paper presents artworks I have made and statements from other artists that exemplify some of PP's core principles. But it also raises questions about the extent to which current applications of PP theory provide a comprehensive account of art experience. Prediction error minimization, a key mechanism of PP, has been proposed as a cause of positive aesthetic affect because artworks offer opportunities for reward through disambiguation and learning. However, there are many cases where prediction errors proliferate in art experiences in a way that enhances aesthetic affect. Here I suggest the inability of our perceptual systems to minimize prediction errors when beholding certain artworks can evoke heightened states of fascination and exhilaration. Moreover, powerful artworks provide opportunities for maximizing prediction errors, within certain bounds, by evoking states of paradox, contradiction and illogicality. I conclude that beholding such artworks can intensify our sense of being by making us more alive to the world. This article is part of the theme issue 'Art, aesthetics and predictive processing: theoretical and empirical perspectives'.

A hole in a piece of cardboard and predictive brain: the incomprehension of modern art in the light of the predictive coding paradigm.

Incomprehension of and resistance to contemporaneous art have been constant features in the development of modern art. The predictive coding framework can be used to analyse this response by outlining the difference between the misunderstanding of (i) contemporary conceptual/minimalist art and (ii) early modern avant-garde art and by elucidating their underlying cognitive mechanisms. In both of these cases, incomprehension and its behavioural consequences are tied to the failure of the optimal prediction error (PE) minimization that is involved in the perception of such art works. In the case of contemporary conceptual/minimalist art the failure stems from the fact that the encounter results in non-salient visual sensations and generates no PE. In early modern avant-garde art, the occasional inability of viewers to recognize pictorial content using new pictorial conventions reflected the absence of suitable priors to explain away ambiguous sensory data. The capacity to recognize pictorial content in modernist painting, as a prerequisite for a satisfying encounter with such works and ultimately a wider acceptance of new artistic styles, required an updating of a number of expectations in order to optimize the fit between priors and sensations, from low-level perceptual priors to the development of higher-level, culturally determined expectations. This article is part of the theme issue 'Art, aesthetics and predictive processing: theoretical and empirical perspectives'.

Soil-Matric-Potential-Based Irrigation Scheduling to Increase Yield and Water Productivity of Okra

A field experiment was conducted on okra (Abelmoschus esculentus L.) for assessing the sustainability of yield with optimum irrigation schedule based on soil moisture depletion. Four irrigation treatments: Irrigation at I1:20%, I2:30%, I3:40% and I4:50% of soil moisture depletion rate in main plots and three fertilizer treatments: Fertigation at F1:100%, F2:80% and F3:60% of recommended NPK (100:25:40 kg/ha) in subplots were tested. Soil matric potential was recorded continuously using electronic tensiometers. The soil moisture characteristics curve was derived for various soil matric potential value sand the soil water content. The irrigation controller triggered solenoid valves for irrigation when soil moisture depletion reached a prespecified level in each treatment. Soil moisture depletion values were significantly predicted based on a regression model calibrated for each treatment over the crop growing period. The model gave minimum prediction error (PE) for I1, followed by I2, I3 and I4, respectively. Plant growth and yield parameters were significantly influenced by the soil moisture availability under each treatment. It is recommended that irrigation be scheduled at 20% soil moisture depletion rate together with 100% NPK fertilizer application for attaining sustainable yield of okra (12.3 t/ha), apart from maximum WUE (3.5 kg/m3) and plant growth parameters under semiarid inceptisols.

Interval models for uncertainty analysis and degradation prediction of the mechanical properties of rubber

Abstract As rubber is a hyperelastic material, its nonlinear deformation behavior during aging is significantly influenced by various factors, including the material characteristics, demonstrating a significant uncertainty. Most of the existing uncertain prediction methods of rubber nonlinear property degradation are based on the probability density function, which requires a large number of samples to obtain the probability distribution and requires a lot of work. Therefore, the interval model is used in this study to characterize the uncertainty. However, the traditional interval constitutive models ignore the correlation between interval variables, and the prediction results have large errors. In order to minimize prediction errors and improve prediction accuracy, an interval Mooney–Rivlin (M–R) correlation model that considers the correlation between parameters was established. To address the influence of uncertainties, an interval Arrhenius model was constructed. The M–R model requires multiple fittings of stress–strain curves to obtain the model parameters, and the prediction process is relatively complex. Therefore, combing the two proposed models, the relationship equations of rubber tensile stress with aging temperature and aging time were first established by interval Arrhenius, and then the interval M–R model was used to obtain the variation ranges of parameters C 10 {C}_{10} and C 01 {C}_{01} . By contrasting this with the measured rubber aging information, the effectiveness of the proposed model was confirmed. Compared with the prediction model based on the average value, the maximum error of prediction of this model is reduced by about 60%. Compared with the traditional interval model, the prediction region is significantly reduced, which further improves the prediction accuracy. The above results indicate that this interval aging lifetime prediction model is suitable for characterizing the nonlinear stress–strain behavior of rubber-like elastomers.

Road surface damages allocation with RTI-IMS software based on YOLO V5 model

ABSTRACT Research on applying artificial intelligence to autonomously detect road surface damages contributes positively to road traffic maintenance and management. This study introduces the Road Traffic Infrastructure Intelligent Management System (RTI IMS) software, utilizing the Yolo V5 programming platform. This software is designed to automatically identify road surface damages during operation. Based on machine learning image recognition technology, the model is trained with a diverse database of road surface damage images from Japan, India, and Vietnam. Additionally, to improve the inference efficiency of the RTI IMS software, the study uses the Mosaic method, tripling the variation to diversify input data during training, thereby minimizing prediction errors. The research results in the successful development of the RTI IMS software, capable of autonomously detecting road surface damages and providing corresponding images to traffic management authorities. This study significantly contributes to the modernization of current road traffic management practices.

GPCR molecular dynamics forecasting using recurrent neural networks

G protein-coupled receptors (GPCRs) are a large superfamily of cell membrane proteins that play an important physiological role as transmitters of extracellular signals. Signal transmission through the cell membrane depends on conformational changes in the transmembrane region of the receptor, which makes the investigation of the dynamics in these regions particularly relevant. Molecular dynamics (MD) simulations provide a wealth of data about the structure, dynamics, and physiological function of biological macromolecules by modelling the interactions between their atomic constituents. In this study, a Recurrent and Convolutional Neural Network (RNN) model, namely Long Short-Term Memory (LSTM), is used to predict the dynamics of two GPCR states and three specific simulations of each one, through their activation path and focussing on specific receptor regions. Active and inactive states of the GPCRs are analysed in six scenarios involving APO, Full Agonist (BI 167107) and Partial Inverse Agonist (carazolol) of the receptor. Four Machine Learning models with increasing complexity in terms of neural network architecture are evaluated, and their results discussed. The best method achieves an overall RMSD lower than 0.139 Å and the transmembrane helices are the regions showing the minimum prediction errors and minimum relative movements of the protein.

A Comparative Study of Statistical and Deep Learning Model-Base weather Prediction in Albania

Rainfalls are one of the most important climate variables that today impact significantly different sectors like agriculture, energy, industry, and so on. Agriculture is one of the most sensitive sectors to climate change because rainfalls in this case, directly affect the positive progress of corps activity. In this case, forecasting rainfalls would help farmers to effectively survive the increasing occurrence of extreme weather events, plan their farming activities, and reduce costs. On the other hand, circular economy (CE) promises a strategy to support sustainable and regenerative agriculture by supporting the sustainable management of water based on water resources. This paper aims to determine the best method for forecasting a natural phenomenon such as the rainfall, that today in Albania, as a result of the unpredictable flows that it often has, is a major problem in the field of agriculture. In this study, the rainfall model based on statistical methods, Auto-Regressive Integrated Moving Average (ARIMA), Error, Trend & Seasonal (ETS) and deep learning models, Long Short-Term Memory Network (LSTM), and Deep Forward Neural Network (DFNN) was developed. The study area that will be used for rainfall forecasting is Albania with a time interval between January 1901 and December 2022. The period that will be used for prediction will be January 2023- December 2024. The performance of each of the models used has been evaluated by using Root Mean Square Error (RMSE) where we also used the comparison of training and validation loss curves to analyze and avoid the model overfitting in the training phase. The results showed that from the comparison between ARIMA and ETS, ETS has the minimum prediction error value while between LSTM and DFNN, DFNN has the best performance in the evaluation metrics (RMSE) and with the best training and validation loss curves. From the final comparison, ETS was better than the DFNN model with the lowest root mean square error (RMSE). ETS was the best model and provided higher accuracy in precipitation forecast.

Development of comprehensive calibration models for pulp traits by near infrared spectroscopy (NIRS) for pure species and hybrids of Corymbia and Eucalyptus

Corymbia hybrid has emerged as a complimentary pulpwood in India along with Eucalyptus camaldulensis and eucalypt hybrids for enhancing the profitability of the industry and the income of farmers. Near infrared spectroscopy (NIRS) offers a rapid non-destructive method for estimating wood and pulp traits of short rotation trees. Development of NIR calibration models in Corymbia is essential for quick selection and rapid advancement of pulp wood traits. A study was carried out to develop a combined calibration curve for pure E. camaldulensis and Corymbia species and their interspecific hybrids. Wood samples were extracted from four-year-old 300 trees of Corymbia torelliana (CT), C. citriodora (CC), C. variegata (CV) and E. camaldulensis (EC) and their interspecific hybrids from progeny evaluation trials at three different locations in south India. The wood logs and powdered core samples were analyzed for kraft pulp yield (KPY), lignin and S|G ratio by wet chemistry and NIRS method. The KPY values of CC and CV ranged from 44 to 52%, whereas CT, a maternal parent in CT x CC|CV hybrids, had a narrow range of 38-46.5%. However, the interspecific hybrids of CT x CC|CV exhibited a range with higher values from 48.5 to 50.5%, indicating a narrow scope for predicting hybrids from that of parent’s standard calibration curves. The estimated values in pure species of Corymbia for lignin content ranged from 22.7 to 29.2 % and 1.9 to 3.1 for S|G ratio, while in hybrids it was 25.6 to 29.4 for lignin. The correlation coefficients for cross-validation of KPY in CC, CV, CT and their hybrids were 0.8, 0.81, 0.89 and 0.72, respectively, and root mean square errors (RMS) were 0.8, 0.55, 0.73 and 0.31, respectively. When CC and CV samples were pooled to generate a common prediction model, the correlation coefficients were 0.8 for KPY, 0.75 for lignin and 0.83 for S|G ratio, with RMS of 0.68 for both KPY and lignin, and 0.12 for S|G ratio. Corymbia hybrids were evaluated with 99% accuracy using a combined prediction model of pure Corymbia species and hybrids. The method was validated with 80 samples of pure species and hybrids with a RMS of less than 1.0. We also attempted in developing a combined prediction model for different species of Corymbia, Eucalyptus, and their hybrids with minimum prediction errors.

Cost Prediction in Blockchain-Enabled Pharmaceutical Supply Chain under Uncertain Demand

Cost prediction can provide a pharma supply chain industry with completing their projects on schedule and within budget. This paper provides a new multi-function Blockchain Technology-enabled Pharmaceutical Supply Chain (BT-enabled PSC) mathematical cost model, including PSC costs, BT costs, and uncertain demand. The purpose of this study is to find the most appropriate algorithm(s) with minimum prediction errors to predict the costs of the BT-enabled PSC model. This paper also aims to determine the importance and cost of each component of the multi-function model. To reach these goals, we combined four Supervised Learning algorithms (KNN, DT, SVM, and NB) with two Evolutionary Computation algorithms (HS and PSO) after data generation. Each component of the multi-function model has its importance, and we applied the Feature Weighting approach to analyze their importance. Next, four performance metrics evaluated the multi-function model, and the Total Ranking Score determined predictive algorithms with high reliability. The results indicate the HS-NB and PSO-NB algorithms perform better than the other six algorithms in predicting the costs of the multi-function model with small errors. The findings also show that the Raw Materials cost has a more substantial influence on the model than the other components. This study also introduces the components of the multi-function BT-enabled PSC model.

Enhancing Traffic Density Detection and Synthesis through Topological Attributes and Generative Methods

This study investigates the utilization of Graph Neural Networks (GNNs) within the realm of traffic forecasting, a critical aspect of intelligent transportation systems. The accuracy of traffic predictions is pivotal for various applications, including trip planning, road traffic control, and vehicle routing. The research comprehensively explores three notable GNN architectures—Graph Convolutional Networks (GCNs), GraphSAGE (Graph Sample and Aggregation), and Gated Graph Neural Networks (GGNNs)—specifically in the context of traffic prediction. Each architecture's methodology is meticulously examined, encompassing layer configurations, activation functions, and hyperparameters. With the primary aim of minimizing prediction errors, the study identifies GGNNs as the most effective choice among the three models. The outcomes, presented in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), reveal intriguing insights. While GCNs exhibit an RMSE of 9.25 and an MAE of 8.2, GraphSAGE demonstrates improved performance with an RMSE of 8.5 and an MAE of 7.6. Gated Graph Neural Networks (GGNNs) emerge as the leading model, showcasing the lowest RMSE of 9.2 and an impressive MAE of 7.0. However, the study acknowledges the dynamic nature of these results, emphasizing their dependency on factors such as the dataset, graph structure, feature engineering, and hyperparameter tuning.

Predictive coding I: Introduction

AbstractPredictive coding – sometimes also known as ‘predictive processing’, ‘free energy minimisation’, or ‘prediction error minimisation’ – claims to offer a complete, unified theory of cognition that stretches all the way from cellular biology to phenomenology. However, the exact content of the view, and how it might achieve its ambitions, is not clear. This series of articles examines predictive coding and attempts to identify its key commitments and justification. The present article begins by focusing on possible confounds with predictive coding: claims that are often identified with predictive coding, but which are not predictive coding. These include the idea that the brain employs an efficient scheme for encoding its incoming sensory signals; that perceptual experience is shaped by prior beliefs; that cognition involves minimisation of prediction error; that the brain is a probabilistic inference engine; and that the brain learns and employs a generative model of the world. These ideas have garnered widespread support in modern cognitive neuroscience, but it is important not to conflate them with predictive coding.

Optimization of Autoclave Reactors to Improve Bearing Life Using the Taguchi Method and the Response Surface Methodology

Plastic pervasiveness in daily life has increased in tandem with population growth. Ethylene–vinyl acetate (EVA) is emerging as a popular compound for manufacturing plastic, which is obtained from ethylene and vinyl acetate synthesis. EVA is produced using autoclave reactors, which often encounter bearing damage under specific operating conditions. This research aims to optimize the parameters in autoclave reactors to enhance bearing life. The study focuses on two crucial factors: the number of impellers and the temperature, with bearing life as the response variable. Simulations using finite-element analysis were conducted to obtain the fatigue life of bearings and validated using real-time company data stating the damage of bearings within 80 days. The optimization process employed the Taguchi method (TM) and the response surface methodology (RSM). A comparison of these techniques revealed that temperature had the most significant influence on the response. Interestingly, both methods yielded the same optimal parameters: seven impellers and a temperature of 150 °C. The simulation results using these optimized parameters demonstrated a noteworthy 3.095% increase in bearing life compared to the initial design. The RSM outperformed the Taguchi method in accurately predicting response values with minimum prediction error under optimal conditions.

Prediction of Q-Band Rain Attenuation Statistics Using Frequency Scaling Models for Temperate Location, Vigo, Spain

The prediction of yearly rain attenuation statistics at Q-band is made from Ka-band measurement for a temperate location, Vigo, Spain, using different frequency scaling models. The validity of the different frequency scaling models is tested for the present location by graphical comparison between measurement and prediction and also in terms of mean, standard deviation, and root mean square errors (RMSE). The Battesti model performs better compared to other existing frequency scaling models, RMSE is only 4.16% and 5.52% for the periods July 2016 to June 2017 and July 2017 to June 2018 respectively. The proposed new power law model increases the accuracy of the prediction for which the RMSE error is 1.09% and 2.17% less compared to the Battesti model for the periods July 2016 to June 2017 and July 2017 to June 2018, respectively. In predicting monthly statistics, the proposed model performs better compared to the Battesti model for all the months except December, January, and February. While predicting monthly statistics, for the proposed model, the maximum and minimum prediction errors are 18.50% and 0.39%, respectively. For the prediction of diurnal statistics, the proposed model performs better compared to the Battesti model with a very small prediction error, less than 4% for both days. The present study can be useful in the design and planning of satellite communication links in present or similar climatic regions for estimating rain attenuation at Q band or above, for which the experimental setup's cost is very high and requires a large receiver margin.

Comprehension and production of Kinyarwanda verbs in the Discriminative Lexicon

Abstract The Discriminative Lexicon is a theory of the mental lexicon that brings together insights from various other theories: words are the relevant cognitive units in morphology, the meaning of a word is represented by its distribution in utterances, word forms and their meaning are learned by minimizing prediction errors, and fully connected networks successfully capture language learning. In this article we model comprehension and production of Kinyarwanda verb forms in the Discriminative Lexicon model. Kinyarwanda is a highly inflectional language, and therefore particularly interesting, because its paradigms are almost unlimited in size. Can knowledge of its enormous paradigms be modeled only on the basis of words? To answer this question we modeled a data set of 11,528 verb forms, hand-annotated for meaning and their grammatical functions, in the Linear Discriminative Learning (LDL), a two-layered, fully connected computational implementation of the Discriminative Lexicon model. We also extracted 573 verbs from our data set for which meanings are available that are based on empirical word embeddings obtained from large text corpora, and modeled them in LDL. Both comprehension and production is learned accurately: Kinyarwanda verb forms can be comprehended and produced relying on words as cognitive units, in a two-layered network, in which prediction errors are minimized.

A Dual-Stage Solar Power Prediction Model That Reflects Uncertainties in Weather Forecasts

Renewable energy sources are being expanded globally in response to global warming. Solar power generation is closely related to solar radiation and typically experiences significant fluctuations in solar radiation hours during periods of high solar radiation, leading to substantial inaccuracies in power generation predictions. In this paper, we suggest a solar power generation prediction method aimed at minimizing prediction errors during solar time. The proposed method comprises two stages. The first stage is the construction of the Solar Base Model by extracting characteristics from input variables. In the second stage, the prediction error period is detected using the Solar Change Point, which measures the difference between the predicted output from the Solar Base Model and the actual power generation. Subsequently, the probability of a weather forecast state change within the error occurrence period is calculated, and this information is used to update the power generation forecast value. The performance evaluation was restricted to July and August. The average improvement rate in predicted power generation was 24.5%. Using the proposed model, updates to weather forecast status information were implemented, leading to enhanced accuracy in predicting solar power generation.

Short-Term Electricity Demand Forecasting Using Deep Neural Networks: An Analysis for Thai Data

Electricity demand forecasting plays a significant role in energy markets. Accurate prediction of electricity demand is the key factor in optimizing power generation and consumption, saving energy resources, and determining energy prices. However, integrating energy mix scenarios, including solar and wind power, which are highly nonlinear and seasonal, into an existing grid increases the uncertainty of generation, creating additional challenges for precise forecasting. To tackle such challenges, state-of-the-art methods and algorithms have been implemented in the literature. Artificial Intelligence (AI)-based deep learning models can effectively handle the information of long time-series data. Based on patterns identified in datasets, various scenarios can be developed. In this paper, several models were constructed and tested using deep AI networks in two different scenarios: Scenario1 used data for weekdays, excluding holidays, while Scenario2 used the data without exclusion. To find the optimal configuration, the models were trained and tested within a large space of alternative hyperparameters. We used an Artificial Neural Network (ANN)-based Feedforward Neural Network (FNN) to show the minimum prediction error for Scenario1 and a Recurrent Neural Network (RNN)-based Gated Recurrent Network (GRU) to show the minimum prediction error for Scenario2. From our results, it can be concluded that the weekday dataset in Scenario1 prepared by excluding weekends and holidays provides better forecasting accuracy compared to the holistic dataset approach used in Scenario2. However, Scenario2 is necessary for predicting the demand on weekends and holidays.

A reduced-rank approach to predicting multiple binary responses through machine learning

This paper investigates the problem of simultaneously predicting multiple binary responses by utilizing a shared set of covariates. Our approach incorporates machine learning techniques for binary classification, without making assumptions about the underlying observations. Instead, our focus lies on a group of predictors, aiming to identify the one that minimizes prediction error. Unlike previous studies that primarily address estimation error, we directly analyze the prediction error of our method using PAC-Bayesian bounds techniques. In this paper, we introduce a pseudo-Bayesian approach capable of handling incomplete response data. Our strategy is efficiently implemented using the Langevin Monte Carlo method. Through simulation studies and a practical application using real data, we demonstrate the effectiveness of our proposed method, producing comparable or sometimes superior results compared to the current state-of-the-art method.