scholarly journals Power Prior Elicitation in Bayesian Quantile Regression

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Rahim Alhamzawi ◽  
Keming Yu
Keyword(s):  
Quantile Regression ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Real Data ◽  
Laplace Distribution ◽  
Scale Mixture ◽  
Prior Elicitation ◽  
Bayesian Quantile Regression ◽  
Critical Issues ◽  
Power Prior

We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data.

scholarly journals A Note on the Hierarchical Model and Power Prior Distribution in Bayesian Quantile Regression

2014 ◽  
Vol 20 (76) ◽  
pp. 1
Author(s):  
طاهر ريسان دخيل
Keyword(s):  
Quantile Regression ◽  
Hierarchical Model ◽  
Prior Distribution ◽  
Hierarchical Models ◽  
Real Data ◽  
Power Parameter ◽  
Bayesian Quantile Regression ◽  
Power Prior

  In this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the  and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.

scholarly journals Improved local quantile regression

2018 ◽  
Vol 19 (5) ◽  
pp. 501-523
Author(s):  
Xi Liu ◽  
Keming Yu ◽  
Qifa Xu ◽  
Xueqing Tang
Keyword(s):  
Quantile Regression ◽  
Real Data ◽  
Laplace Distribution ◽  
Regression Method ◽  
Simulation Studies ◽  
Weighted Likelihood ◽  
Scale Mixture ◽  
Good Design ◽  
Statistical Planning ◽  
Quantile Regression Method

We investigate a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of asymmetric Laplace distribution (ALD). This approach enjoys the same good design adaptation as the local quantile regression ( Spokoiny et al., 2013 , Journal of Statistical Planning and Inference, 143, 1109–1129), particularly for smoothing extreme quantile curves, and ensures non-crossing quantile curves for any given sample. The performance of the proposed method is evaluated via extensive Monte Carlo simulation studies and one real data analysis.

scholarly journals Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

CAUCHY ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 121
Author(s):  
Catrin Muharisa ◽  
Ferra Yanuar ◽  
Dodi Devianto
Keyword(s):  
Confidence Interval ◽  
Quantile Regression ◽  
Simulation Study ◽  
Likelihood Function ◽  
Laplace Distribution ◽  
Regression Method ◽  
Bayesian Regression ◽  
Asymmetric Laplace Distribution ◽  
Bayesian Quantile Regression ◽  
Quantile Regression Method

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. <strong>Method: </strong>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. <strong>Result: </strong>Bayesian quantile regression method results has more significance parameter and smaller confidence interval than quantile regression method. <strong>Conclusion: </strong>This study proves that Bayesian quantile regression method can produce acceptable parameter estimate for nonnormal error.

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

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 118-128
Author(s):  
Ferra Yanuar ◽  
Athifa Salsabila Deva ◽  
Maiyastri Maiyastri
Keyword(s):  
Quantile Regression ◽  
Hospital Stay ◽  
Bayesian Approach ◽  
Likelihood Function ◽  
Length Of Hospital Stay ◽  
Regression Method ◽  
Bayesian Quantile Regression ◽  
West Sumatra ◽  
Quantile Regression Method ◽  
The Bayesian 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.

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

2017 ◽  
Vol 18 (1) ◽  
pp. 73-93 ◽  
Author(s):  
Bruno Santos ◽  
Heleno Bolfarine
Keyword(s):  
Regression Analysis ◽  
Quantile Regression ◽  
Durable Goods ◽  
Continuous Distribution ◽  
Real Data ◽  
Discrete Component ◽  
Bayesian Quantile Regression ◽  
Conditional Quantiles ◽  
Quantile Regression Analysis ◽  
Quantile Regression Method

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.

scholarly journals A Discrete Density Approach to Bayesian Quantile and Expectile Regression with Discrete Responses

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Xi Liu ◽  
Xueping Hu ◽  
Keming Yu
Keyword(s):  
Quantile Regression ◽  
Regression Models ◽  
Likelihood Function ◽  
Real Data ◽  
Model Parameters ◽  
Expectile Regression ◽  
Improper Priors ◽  
Continuous Responses ◽  
Discrete Responses ◽  
Probability Mass

AbstractFor decades, regression models beyond the mean for continuous responses have attracted great attention in the literature. These models typically include quantile regression and expectile regression. But there is little research on these regression models for discrete responses, particularly from a Bayesian perspective. By forming the likelihood function based on suitable discrete probability mass functions, this paper introduces a discrete density approach for Bayesian inference of these regression models with discrete responses. Bayesian quantile regression for discrete responses is first developed, and then this method is extended to Bayesian expectile regression for discrete responses. The posterior distribution under this approach is shown not only coherent irrespective of the true distribution of the response, but also proper with regarding to improper priors for the unknown model parameters. The performance of the method is evaluated via extensive Monte Carlo simulation studies and one real data analysis.

Sign in / Sign up

Export Citation Format

Share Document