Bayesian Quantile Regression Research Articles

Teleconnections between oceanic–atmospheric indices and drought over Iran using quantile regressions

ABSTRACT In this research, the Bayesian quantile regression model is applied to investigate the teleconnections between large oceanic–atmospheric indices and drought standardized precipitation index (SPI) in Iran. The 12-month SPI time series from 138 synoptic stations for 1952–2014 were selected as the drought index. Three oceanic–atmospheric indices, the North Atlantic Oscillation (NAO), the Southern Oscillation Index (SOI) and the Multivariate El Niño/Southern Oscillation Index (MEI), were selected as covariates. The results show that NAO has the weakest impact on drought in different quantiles and different regions in Iran. La Niña conditions amplified droughts through all SPI quantiles in western, Caspian Sea coastal regions and southern regions. The positive phase of MEI significantly modulates low SPI quantiles (i.e. drought conditions) throughout the Zagros region, Caspian Sea coastal regions and southern regions. The study shows that the effect of large oceanic–atmospheric indices have heterogeneous impacts on extreme dry and wet conditions.

Research on Comprehensive Development of Shandong Province Based on Bayesian Quantile Regression

Based on the theme of coordinated development in Shandong Province, the article proposes coordinated indicators based on the three aspects of economy, society and ecology, and uses the principal component analysis method and entropy method to integrate the three aspects of economy, society and ecology in Shandong The indicators were selected. Then the Bayesian quantile model was used to construct an evaluation model and the coordinated development of Shandong Province was evaluated. It shows that Shandong Province needs to vigorously develop ecology and vigorously develop indicators that affect Shandong Province’s great changes if it wants to rapidly increase its comprehensive strength.

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.

The Dynamic Correlation Between Capital Deepening and Total Factor Productivity in China

The impact of capital deepening on total factor productivity (TFP) is a significant and controversial issue. Based on the calculation of relevant indicators, this study adopts a Bayesian time-varying parameter model, Bayesian quantile regression, and adaptive Bayesian quantile models for in-depth statistical analysis. TFP was found to have a complex non-linear structure, and physical and human capital deepening indicators show a significant upward trend. The deepening of physical capital has a negative impact on TFP, while the deepening of human capital has a positive impact. In the capital deepening structure, the level of TFP has been improved and its structure optimized. Primary human and non-production physical capital deepening has no significant effect on TFP, while secondary human capital deepening has some significant effects on TFP. Tertiary and productive human capital deepening of TFP present two different forms of significant effect: the influence coefficient of the former declines in the increasing quantile and the change is larger, while the latter has a stable negative impact. The results of this study provide insights in terms of the improvement of China’s productivity.

Measuring the effects of inflation and inflation uncertainty on output growth in the central and eastern European countries

ABSTRACT This paper investigates how inflation and its uncertainty impact GDP growth in eight Central and Eastern European Countries. Inflation uncertainty series are created examining several GARCH models in combination with three different distribution functions, while the nonlinear effect of inflation and its uncertainty on GDP growth is assessed in the Bayesian quantile regression framework. We find that inflation has significantly smaller negative effect on GDP growth than inflation uncertainty, which confirms the Friedman hypothesis. This means that inflation in the selected countries has an indirect impact on GDP growth via inflation uncertainty. We find that countries with smaller economy, such as Latvia and Estonia experience more adverse effect from inflation uncertainty in both upturn and downturn conditions, probably because they are vulnerable to external inflationary shocks. As for the countries with bigger economy, inflation uncertainty shocks diminish GDP growth only in conditions when output growth is very low or negative.

Bayesian Multiple Quantile Regression for Linear Models Using a Score Likelihood

We propose the use of a score based working likelihood function for quantile regression which can perform inference for multiple conditional quantiles of an arbitrary number. We show that the proposed likelihood can be used in a Bayesian framework leading to valid frequentist inference, whereas the commonly used asymmetric Laplace working likelihood leads to invalid interval estimations and requires further correction. For computation, we propose a novel adaptive importance sampling algorithm to compute important posterior summaries such as the posterior mean and the covariance matrix. Our proposed approach makes it feasible to perform valid inference for parameters such as the slope differences at different quantile levels, which is either not possible or cumbersome using existing Bayesian approaches. Empirical results demonstrate that the proposed likelihood has good estimation and inferential properties and that the proposed computational algorithm is more efficient than its competitors.

Incorporating side information into Robust Matrix Factorization with Bayesian Quantile Regression

Matrix Factorization is a widely used technique for modeling pairwise and matrix-like data. It is frequently used in pattern recognition, topic analysis and other areas. Side information is often available, however utilization of this additional information is problematic in the pure matrix factorization framework. This article proposes a novel method of utilizing side information by combining arbitrary nonlinear Quantile Regression model and Matrix Factorization under Bayesian framework. Gradient-free optimization procedure with the novel Surrogate Function is used to solve the resulting MAP estimator. The model performance has been evaluated on real data-sets.

Changes in extreme rainfall and its implications for design rainfall using a Bayesian quantile regression approach

Abstract This study aims to explore possible distributional changes in annual daily maximum rainfalls (ADMRs) over South Korea using a Bayesian multiple non-crossing quantile regression model. The distributional changes in the ADMRs are grouped into nine categories, focusing on changes in the location and scale parameters of the probability distribution. We identified seven categories for a distributional change in the selected stations. Most of the stations (28 of 50) are classified as Category III, which is characterized by an upward trend with an increase in variance in the distribution. Moreover, stations with a downward trend with a decrease in the variance pattern (Category VII) are mainly distributed on the southern Korean coast. On the other hand, Category I stations are mostly located in eastern Korea and primarily show a statistically significant upward trend with a decrease in variance. Moreover, this study explored changes in design rainfall estimates for different categories in terms of distributional changes. For Categories I, II, III, and VI, a noticeable increase in design rainfall was observed, while Categories IV, V, and VII showed no evidence of association with risk of increased extreme rainfall.

What Bayesian quantiles can tell about volatility transmission between the major agricultural futures?

This paper investigates an idiosyncratic volatility spillover effect between the four agricultural futures – corn, wheat, soybean, and rise. In order to avoid biased measurements of the volatilities, we use the Markov switching generalized autoregressive conditional heteroskedasticity (MS-GARCH) model. The created volatilities are imbedded in the Bayesian quantile regression framework which can produce accurate quantile estimates. We report that soybean and wheat receive relatively high levels of volatility shocks from the other markets, and that excludes soybean and wheat as primary investment assets in a portfolio. On the other hand, rice receives the lowest amount of volatility shocks from all other agricultural futures. The reason could be the policy of rice price stability that is conducted by countries in the Asia and Pacific region. This result favours rice futures, from the four commodities, as the primary asset in a portfolio. All other futures are suitable to be an auxiliary asset in a portfolio with rice, because rice receives the weakest volatility shocks spillover effect from the other three markets.

Genus-level change in aggressiveness with continuous invasions: a phylogenetically-informed Bayesian quantile regression

Phytophthora is a genus of oomycete plant pathogens consisting of numerous invaders of production and natural systems. To date, only few studies assessed how invasions change over time, and none have examined changes in invasive genera consisting of multiple species. With increasing globalisation, pathogens invade and adapt to new environments and hosts. After establishment, the aggressiveness of pathogens could decrease due to biotic and abiotic factors. Conversely, highly pathogenic genotypes should continuously replace less pathogenic ones. Here, we compiled the disease development data of Phytophthora species from published data and reports that span 105 years to assess how aggressiveness has changed over time. For each aggressiveness trial, we recorded the year of pathogen isolation and a measure of pathogenicity, as well as local environmental variables. Phylogenetic multi-level quantile regression was used to analyse the relationships between aggressiveness and time across pathogen taxa under different environmental conditions. We found that aggressiveness decreased over time. This holds true if only the most commonly isolated taxa, and the most recent isolates, were considered. Highly aggressive pathogens from agriculture and natural ecosystems decreased significantly. However, pathogens from nurseries generally became more aggressive over time, particularly among the most common species. Phytophthora diseases overall are highly pathogenic and have potential to cause outbreaks, especially given that the common species were more aggressive under higher temperature variability. Through a multi-level approach, we uncover how the aggressiveness of pathogens changes globally at the genus-level with continuous emergence and invasion.

Noncrossing structured additive multiple-output Bayesian quantile regression models

Quantile regression models are a powerful tool for studying different points of the conditional distribution of univariate response variables. Their multivariate counterpart extension though is not straightforward, starting with the definition of multivariate quantiles. We propose here a flexible Bayesian quantile regression model when the response variable is multivariate, where we are able to define a structured additive framework for all predictor variables. We build on previous ideas considering a directional approach to define the quantiles of a response variable with multiple outputs, and we define noncrossing quantiles in every directional quantile model. We define a Markov chain Monte Carlo (MCMC) procedure for model estimation, where the noncrossing property is obtained considering a Gaussian process design to model the correlation between several quantile regression models. We illustrate the results of these models using two datasets: one on dimensions of inequality in the population, such as income and health; the second on scores of students in the Brazilian High School National Exam, considering three dimensions for the response variable.

Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions

A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR’s conditional mean. Even though the one-step-ahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs’ established performance for forecasting and structural analysis.

Bayesian bent line quantile regression model

This article introduces a Bayesian estimating method for a bent line quantile regression model. Within the Bayesian framework, regression coefficients and threshold can be simultaneously estimated, addressing the problem of optimizing the loss function in frequentist approaches, while the statistical inference on the threshold is direct. Simulation studies and two real data examples show that the Bayesian method demonstrates better sample performance.

Identification of Wiener Model with Internal Noise Using a Cubic Spline Approximation-Bayesian Composite Quantile Regression Algorithm

A cubic spline approximation-Bayesian composite quantile regression algorithm is proposed to estimate parameters and structure of the Wiener model with internal noise. Firstly, an ARX model with a high order is taken to represent the linear block; meanwhile, the nonlinear block (reversibility) is approximated by a cubic spline function. Then, parameters are estimated by using the Bayesian composite quantile regression algorithm. In order to reduce the computational burden, the Markov Chain Monte Carlo algorithm is introduced to calculate the expectation of parameters’ posterior distribution. To determine the structure order, the Final Output Error and the Akaike Information Criterion are used in the nonlinear block and the linear block, respectively. Finally, a numerical simulation and an industrial case verify the effectiveness of the proposed algorithm.

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.

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.

Reducing the risk in tail risk forecasting models

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, a new additive-type model is developed for the ES component that is robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.

一种基于ALD和AEP分布的贝叶斯分位数回归

一种基于ALD和AEP分布的贝叶斯分位数回归

Comparative analysis of Bayesian quantile regression models for pedestrian injury severity at signalized intersections

This study intended to (1) investigate the pedestrian injury severity involved in traffic crashes; and (2) address the heterogeneity issue at signalized intersections. To achieve the objectives, Bayesian binary and ordinal quantile regression models were proposed to address the pedestrian injury severity at signalized intersections. The suitability of the proposed method was illustrated with the Hong Kong dataset from 2008 to 2012 and 376 signalized intersections involving 2090 pedestrian-related crashes are selected. It’s found that age, injury location, pedestrian special circumstance, pedestrian contributory and the presence of Tram/LRT stops and right turning pocket are significant variables. The results indicated that both Bayesian binary and ordinal quantile regression models not only provide a more comprehensive and in-depth understanding of the relationship between pedestrian injury severity and the explanatory variables, but also highlight the heterogeneity issue for the data collected at different locations and different times without many assumptions. The goodness-of-fit of the proposed models outperforms existing mean models, while the Bayesian binary quantile model provides a better fit than the Bayesian quantile regression for ordinal model. The results can benefit the pedestrian facilities improvement/management and guide a much safer pedestrian environment.

Bayesian Regularized Quantile Regression Analysis Based on Asymmetric Laplace Distribution

In recent years, variable selection based on penalty likelihood methods has aroused great concern. Based on the Gibbs sampling algorithm of asymmetric Laplace distribution, this paper considers the quantile regression with adaptive Lasso and Lasso penalty from a Bayesian point of view. Under the non-Bayesian and Bayesian framework, several regularization quantile regression methods are systematically compared for error terms with different distributions and heteroscedasticity. Under the error term of asymmetric Laplace distribution, statistical simulation results show that the Bayesian regularized quantile regression is superior to other distributions in all quantiles. And based on the asymmetric Laplace distribution, the Bayesian regularized quantile regression approach performs better than the non-Bayesian approach in parameter estimation and prediction. Through real data analyses, we also confirm the above conclusions.