Bayesian Quantile Regression Method Research Articles

Analysis of human capital effects introducing Bayesian quantile regression in the process of industrial structural upgrading.

In recent years, with the continuous evolution of the global economy and the adjustment of industrial structures, the understanding of the role played by human capital in the process of economic development has become particularly important. However, existing research on the impact of human capital on economic growth often adopts traditional regression methods, failing to comprehensively consider the heterogeneity and nonlinear relationships in the data. Therefore, to more accurately understand the influence of human capital on economic growth at different stages, this study employs Bayesian quantile regression method (BQRM). By incorporating BQRM, a better capture of the dynamic effects of human capital in the process of industrial structure upgrading is achieved, offering policymakers more targeted and effective policy recommendations to drive the economy towards a more sustainable direction. Additionally, the experiment also examines the impact of other key factors such as technological progress, capital investment, and labor market conditions on economic growth. These factors, combined with human capital, collectively promote the upgrading of industrial structure and the sustainable development of the economy. This study, by introducing BQRM, aims to fill the research gap regarding the impact of human capital on economic development during the industrial structural upgrading process. In the backdrop of the ongoing evolution of the global economy and adjustments in industrial structure, understanding the role of human capital in economic development becomes particularly crucial. To better comprehend the direct impact of human capital, the experiment collected macroeconomic data, including GDP, industrial structure, labor skills, and human capital, from different regions over the past 20 years. By establishing a dynamic panel data model, this study delves into the trends in the impact of human capital at various stages of industrial structure upgrading. The research findings indicate that during the high-speed growth phase, the contribution of human capital to GDP growth is 15.2% ± 2.1%, rising to 23.8% ± 3.4% during the period of industrial structure adjustment. Technological progress, capital investment, and labor market conditions also significantly influence economic growth at different stages. In terms of innovation improvement, this study pioneers the use of BQRM to gain a deeper understanding of the role of human capital in economic development, providing more targeted and effective policy recommendations. Ultimately, to promote sustainable economic development, the experiment proposes concrete and targeted policy recommendations, emphasizing government support in training and skill development. This study not only fills a research gap in the relevant field but also provides substantive references for decision-makers, driving the economy towards a more sustainable direction.

Seasonal relationship between climatic variables and evaporation based on Bayesian quantile regression method in southern Caspian region

Seasonal relationship between climatic variables and evaporation based on Bayesian quantile regression method in southern Caspian region

Modeling Length of Hospital Stay for Patients With COVID-19 in West Sumatra Using Quantile Regression Approach

This study aims to construct the model for the length of hospital stay for patients with COVID-19 using quantile regression and Bayesian quantile approaches. The quantile regression models the relationship at any point of the conditional distribution of the dependent variable on several independent variables. The Bayesian quantile regression combines the concept of quantile analysis into the Bayesian approach. In the Bayesian approach, the Asymmetric Laplace Distribution (ALD) distribution is used to form the likelihood function as the basis for formulating the posterior distribution. All 688 patients with COVID-19 treated in M. Djamil Hospital and Universitas Andalas Hospital in Padang City between March-July 2020 were used in this study. This study found that the Bayesian quantile regression method results in a smaller 95% confidence interval and higher value than the quantile regression method. It is concluded that the Bayesian quantile regression method tends to yield a better model than the quantile method. Based on the Bayesian quantile regression method, it investigates that the length of hospital stay for patients with COVID-19 in West Sumatra is significantly influenced by Age, Diagnoses status, and Discharge status.

Regional Agroclimate Characteristic and Its Multiple Teleconnections: A Case Study in the Jianghan Plain (JHP) Region

Agricultural production depends on local agroclimatic conditions to a great extent, affected by ENSO and other ocean-atmospheric climate modes. This paper analyzed the spatio-temporal distributions of climate elements in the Jianghan Plain (JHP), Central China, and explored the impacts from teleconnection patterns, aimed at providing references for dealing with climate change and guiding agricultural activities. Both linear and multifactorial regression models were constructed based on the frequentist quantile regression and Bayesian quantile regression method, with the daily meteorological data sets of 17 national stations in the plain and teleconnection climate characteristic indices. The results showed that precipitation in JHP had stronger spatial variability than evapotranspiration. El Niño probably induced less precipitation in summer while the weakening Arctic Oscillation might lead to more summertime precipitation. The Nash-Sutcliffe efficiency (NSE) of the multifactorial and linear regression model at the median level were 0.42–0.56 and 0.12–0.18, respectively. The mean relative error (MRE) ranged −2.95–−0.26% and −7.83–0.94%, respectively, indicating the much better fitting accuracy of the multiple climatic factors model. Meanwhile it confirmed that the agricultural climate in JHP was under the influence from multiple teleconnection patterns.

Study on the Level of Talent Attractiveness of the Yangtze River Delta Urban Agglomerations Using Bayesian Quantile Regression Method

Innovation is the first driving force to lead development, and the carrier of innovation drive is talent, and talent has been an important strategic resource to lead social development in the 21st century. And different levels of cities should focus on the strategy of attracting talents. In this paper, based on the index data of the Yangtze River Delta Urban Agglomerations in 2019, we construct the evaluation talent attractiveness level score and use it to build a Bayesian quantile regression model to map the focus that cities of different levels should focus on talent attraction policies. The results show that the marginal gain of talent attraction is different for different level cities in different dimensions. By quantifying the level of talent attractiveness of different cities through the objective assignment method, we find the differences in the spatial distribution of talent attractiveness of different cities in the Yangtze River Delta region and provide theoretical guidance for the integration of the Yangtze River Delta. At the same time, by exploring the differences in the talent attractiveness of cities of different levels that should be focused on, we find the general rules and provide reference and guidance for other cities.

Bayesian quantile regression and unsupervised learning methods to the US Army and Navy data

We apply the Bayesian quantile regression (BayesQR) model for binary response variables and the unsupervised learning methods to synthetic data (Stevens and Anderson-Cook, 2017a, 2017b), which is univariate data with a binary response of passing or failing for complex munitions generated to match age and usage rate found in US Department of Defense complex systems (Army and Navy). Instead of the generalised linear model (GLM) used in Stevens and Anderson-Cook (2017a), we propose to apply the BayesQR to predict a binary response of passing or failing for the Army and Navy data as well as the unsupervised learning methods. First, we want to find the best models for the Army and Navy through comparing statistical inference of BayesQR and GLMs and calculating their percentage correctly classified (PCC) which tests the accuracy of a prediction. The second method focuses on clustering using the k-means clustering and random forests based on the results of BayesQR. We compare models with different covariates to find the one that can best divide data into two groups: Army and Navy.

Simulation Study of Autocorrelated Error Using Bayesian Quantile Regression


 The purpose of this study is to compare the ability of the Classical Quantile Regression method and the Bayesian Quantile Regression method in estimating models that contain autocorrelated error problems using simulation studies. In the quantile regression approach, the data response is divided into several pieces or quantiles conditions on indicator variables. Then, The parameter model is estimated for each selected quantiles. The parameters are estimated using conditional quantile functions obtained by minimizing absolute asymmetric errors. In the Bayesian quantile regression method, the data error is assumed to be asymmetric Laplace distribution. The Bayesian approach for quantile regression uses the Markov Chain Monte Carlo Method with the Gibbs sample algorithm to produce a converging posterior mean. The best method for estimating parameter is the method that produces the smallest absolute value of bias and the smallest confidence interval. This study resulted that the Bayesian Quantile method produces smaller absolute bias values and confidence intervals than the quantile regression method. These results proved that the Bayesian Quantile Regression method tends to produce better estimate values than the Quantile Regression method in the case of autocorrelation errors. 
 Keywords: Quantile Regression Method, Bayesian Quantile Regression Method, Confidence Interval, Autocorrelation.

Friction Characteristics of Post‐Tensioned Tendons of Full‐Scale Structures Based on Site Tests

In the design of prestressing concrete structures, the friction characteristics between strands and channels have an important influence on the distribution of prestressing force, which can be considered comprehensively by curvature and swing friction coefficients. However, the proposed friction coefficient varies widely and may lead to an inaccurate prestress estimation. In this study, four full‐scale field specimens were established to measure the friction loss of prestressing tendons with electromagnetic sensors and anchor cable dynamometers to evaluate the friction coefficient. The least square method and Bayesian quantile regression method were adopted to calculate the friction coefficient, and the results were compared with that in the specifications. Field test results showed that Bayesian quantile regression method was more effective and significant in the estimation of the friction coefficient.

Bayesian Quantile Regression and Unsupervised Learning Methods to the US Army and Navy Data

We apply the Bayesian quantile regression (BayesQR) model for binary response variables and the unsupervised learning methods to synthetic data (Stevens and Anderson-Cook, 2017a, 2017b), which is univariate data with a binary response of passing or failing for complex munitions generated to match age and usage rate found in US Department of Defense complex systems (Army and Navy). Instead of the generalised linear model (GLM) used in Stevens and Anderson-Cook (2017a), we propose to apply the BayesQR to predict a binary response of passing or failing for the Army and Navy data as well as the unsupervised learning methods. First, we want to find the best models for the Army and Navy through comparing statistical inference of BayesQR and GLMs and calculating their percentage correctly classified (PCC) which tests the accuracy of a prediction. The second method focuses on clustering using the k-means clustering and random forests based on the results of BayesQR. We compare models with different covariates to find the one that can best divide data into two groups: Army and Navy.

On the use of Bayesian quantile regression method to explore the historical trends in extreme precipitation and their connections with large-scale climate patterns over the contiguous USA

The probability distribution function (PDF) of precipitation is expected to change under a warmer climate. The existing studies have not been able to detect trends in different thresholds of the PDF of extreme precipitation series for the contiguous USA. In this study, a fresh statistical approach (the Bayesian quantile regression method) was employed to analyze trends of annual daily maximum (ADM) and monthly maximum (MM) precipitation indices at different quantile levels and their teleconnections with large-scale climate patterns over the contiguous USA. Historic precipitation time series over the period of 65 years (1950–2014) for 1108 sites was used for the analysis. To investigate the relations between precipitation and large-scale climate patterns, two major oscillations [the El Nino–Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO)] were used as covariates in the Bayesian quantile regression model. Our results show that changes in upper quantiles of the distributions of the extreme precipitation (for both ADM and MM) have occurred at a much higher rate than previously believed as compared to the lower quantiles mainly in the coastal regions in the eastern half of the country. Variability in the spatial distribution of significant trends was observed when either ENSO or NAO index was used as a covariate in the Bayesian quantile regression model. However, for many regions of the USA, a stronger teleconnection between climate indices and precipitation indices for upper quantile level was observed as compared to lower quantile levels for both ADM and MM. The trends detected using the Bayesian quantile regression method were undetected or overlooked by other previously used approaches for trend detection. Such results are particularly useful for water managers who are more concerned with extreme values rather than the averaged one.

Bayesian Quantile Regression Method to Construct the Low Birth Weight Model

This study aims to implement Bayesian quantile regression method in constructing the model of Low Birth Weight. The data of Low Birth Weight is violated of nonnormal assumption for error terms. This study considers quantile regression approach and use Gibbs sampling algorithm from Bayesian method for fitting the quantile regression model. This study explores the performance of the asymmetric Laplace distribution for working likelihood in posterior estimation process. This study also compare the result of variable selection in quantile regression and Bayesian quantile regression for Low Birth Weight model. This study. proved that Bayesan quantile method produced better model than just quantile approach. Bayesian quantile method proved that it can handle the nonnormal problem although using moderate size of data.

How Does Industrial Waste Gas Emission Affect Health Care Expenditure in Different Regions of China: An Application of Bayesian Quantile Regression.

Industrial development has brought about not only rapid economic growth, but also serious environmental pollution in China, which has led to serious health problems and heavy economic burdens on healthcare. Therefore, the relationship between the industrial air pollution and health care expenditure (HCE) has attracted the attention of researchers, most of which used the traditional empirical methods, such as ordinary least squares (OLS), logistic and so on. By collecting the panel data of 30 provinces of China during 2005–2016, this paper attempts to use the Bayesian quantile regression (BQR) to reveal the impact of industrial air pollution represented by industrial waste gas emission (IWGE) on HCE in high-, middle-, low-income regions. It was found that double heterogeneity in the influence of IWGE on HCE was obvious, which revealed that people in high-, middle-, low-income regions have significantly different understandings of environmental pollution and health problems. In addition, the BQR method provided more information than the traditional empirical methods, which verified that the BQR method, as a new empirical method for previous studies, was applicable in this topic and expanded the discussion space of this research field.

Projection of Long-Term Care Costs in China, 2020–2050: Based on the Bayesian Quantile Regression Method

The aging population in China highlights the significance of elderly long-term care (LTC) services. The number of people aged 65 and above increased from 96 million in 2003 to 150 million in 2016, some of whom were disabled due to chronic diseases or the natural effects of aging on bodily functions. Therefore, the measurement of future LTC costs is of crucial value. Following the basic framework but using different empirical methods from those presented in previous literature, this paper attempts to use the Bayesian quantile regression (BQR) method, which has many advantages over traditional linear regression. Another innovation consists of setting and measuring the high, middle, and low levels of LTC cost prediction for each disability state among the elderly in 2020–2050. Our projections suggest that by 2020, LTC costs will increase to median values of 39.46, 8.98, and 20.25 billion dollars for mild, moderate, and severe disabilities, respectively; these numbers will reach 141.7, 32.28, and 72.78 billion dollars by 2050. The median level of daily life care for mild, moderate, and severe disabilities will increase to 26.23, 6.36, and 27 billion dollars. Our results showed that future LTC cost increases will be enormous, and therefore, the establishment of a reasonable individual-social-government payment mechanism is necessary for the LTC system. The future design of an LTCI system must take into account a variety of factors, including the future elderly population, different care conditions, the financial burden of the government, etc., in order to maintain the sustainable development of the LTC system.

Bayesian Quantile Regression Methods in Handling Non-normal and Heterogeneous Error Term

Bayesian Quantile Regression Methods in Handling Non-normal and Heterogeneous Error Term

Bayesian Detection of Abnormal Asynchrony of Division Between Sister Cells in Mutant Caenorhabditis elegans Embryos.

Cell division timing is critical for cell fate specification and morphogenesis during embryogenesis, but how division timings are regulated among cells during development is poorly understood. In this article, we focus on the comparison of asynchrony of division, that is, difference of lifetime, between sister cells (ADS) among wild-type and mutant individuals of Caenorhabditis elegans. On the one hand, due to extreme imbalance between wild-type individuals and mutant-type samples, direct comparison of two distributions of ADS between wild type and mutant type is not feasible. On the other hand, we originally found that the ADS is correlated with the lifespan of the corresponding mother cell in wild type. Hence, a semiparametric Bayesian quantile regression method where lifetime of the mother cell is taken as covariate is developed to estimate the 95% confidence curve of ADS in wild type and then ADS of mutant type is classified as abnormal if outside the corresponding confidence interval. A high accuracy of our method is demonstrated by a large-scale simulation study. Real data analysis shows that ADS is related to gene function and expression quantitatively.

Influencing factors of disability among the elderly in China, 2003–2016: application of Bayesian quantile regression

Background: More and more disabled elderly need long-term care as China becomes an aging society. In 2016, there were 220 million people over the age of 60, and nearly 10 million completely disabled elderly people who cannot complete Activities of Daily Living (ADLs). Therefore, the topic of influencing factors for disability among the elderly in China has attracted close attention from researchers, most of which use the traditional empirical methods, such as Ordinary Least Squares (OLS) and logistic.Objective: The purpose of this paper was to introduce the Bayesian Quantile Regression (BQR) method to the topic of the disabled elderly, which was achieved by using BQR to study the influencing factors of disability among the elderly in China during 2003–2016.Methods: This paper was the first attempt to use the BQR for the influencing factors of disability among the elderly in China. Furthermore, a comparison was made between the regression results of BQR, OLS, Quantile Regression (QR), and Bayesian Linear Regression (BLR).Results: It was found that there was a relatively stable relationship between chronic diseases and disability, although there was a little difference in different quantiles. In addition, the BQR can obtain results similar to the traditional method. For instance, the coefficient of chronic diseases (to total disability) obtained by OLS, QR, and BLR were basically consistent (around 0.778), which was similar to BQR. The BQR not only provided estimates for all the quantiles, but also provided upper and lower values of a certain confidence interval.Conclusions: By applying the BQR to the influencing factors of disability among the elderly in China, we reached the conclusion that BQR methods are adaptable for this research topic because of their characteristics and advantages over the traditional methods, such as less strict constraints, the estimates for all quantiles, and the combination of historical information with prior information. Moreover, the BQR method appropriately obtained the lower and upper values in a confidence interval, which can provide prediction space for the future.

Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

The purposes of this paper is to introduce the ability of the Bayesian quantile regression method in overcoming the problem of the nonnormal errors using asymmetric laplace distribution on simulation study. Method: We generate data and set distribution of error is asymmetric laplace distribution error, which is non normal data. In this research, we solve the nonnormal problem using quantile regression method and Bayesian quantile regression method and then we compare. The approach of the quantile regression is to separate or divide the data into any quantiles, estimate the conditional quantile function and minimize absolute error that is asymmetrical. Bayesian regression method used the asymmetric laplace distribution in likelihood function. Markov Chain Monte Carlo method using Gibbs sampling algorithm is applied then to estimate the parameter in Bayesian regression method. Convergency and confidence interval of parameter estimated are also checked. Result: Bayesian quantile regression method results has more significance parameter and smaller confidence interval than quantile regression method. Conclusion: This study proves that Bayesian quantile regression method can produce acceptable parameter estimate for nonnormal error.

Bayesian quantile regression analysis for continuous data with a discrete component at zero

In this work, we propose a Bayesian quantile regression method to response variables with mixed discrete-continuous distribution with a point mass at zero, where these observations are believed to be left censored or true zeros. We combine the information provided by the quantile regression analysis to present a more complete description of the probability of being censored given that the observed value is equal to zero, while also studying the conditional quantiles of the continuous part. We build up a Markov Chain Monte Carlo method from related models in the literature to obtain samples from the posterior distribution. We demonstrate the suitability of the model to analyse this censoring probability with a simulated example and two applications with real data. The first is a well-known dataset from the econometrics literature about women labour in Britain, and the second considers the statistical analysis of expenditures with durable goods, considering information from Brazil.

The Bayesian quantile regression method in accelerated life tests

ABSTRACTIn accelerated life tests (ALT), there are many limitations for a traditional parametric method to estimate a particular quantile in the lower tail of the lifetime distribution at the use condition. This article develops a Bayesian quantile regression method for analyzing ALT data. As a distribution-free method, Bayesian quantile regression method is robust to lifetime distribution uncertainty and flexible to deal with the relationship between shape parameter and accelerating stresses. A Gibbs sampling method is implemented for Bayesian posterior inference. This method is easy to implement and allows us to use data augmentation to simplify the computation in the presence of right-censored observations. A simulation study and a real example are used to demonstrate the advanced properties of proposed method.

Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures

This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature.