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On Bayesian quantile regression and outliers [article]

Bruno Santos, Heleno Bolfarine
2016 arXiv   pre-print
Using a representation of the asymmetric Laplace distribution as a mixture of a normal and an exponential distribution, we discuss the relevance of the presence of a scale parameter to control for the  ...  compare the posterior distribution for each latent variable with the others.  ...  variation and the variation due to the asymmetric Laplace in the likelihood.  ... 
arXiv:1601.07344v1 fatcat:xzg4kywsq5elzhka7legcltx4q

Spatial Quantile Multiple Regression Using the Asymmetric Laplace Process

Kristian Lum, Alan E. Gelfand
2012 Bayesian Analysis  
We work in the context of spatially referenced data and extend the asymmetric Laplace model for quantile regression to a spatial process, the asymmetric Laplace process (ALP) for quantile regression with  ...  By taking advantage of a convenient conditionally Gaussian representation of the asymmetric Laplace distribution, we are able to straightforwardly incorporate spatial dependence in this process.  ...  Acknowledgments The authors thank Marie Lynn Miranda for valuable discussions and the use of the North Carolina birth weight dataset.  ... 
doi:10.1214/12-ba708 fatcat:c6sgq7jk3zd5nkykrnojzvswwe

Posterior Inference for Quantile Regression: Adaptation to Sparsity [article]

Yuanzhi Li, Xuming He
2021 arXiv   pre-print
We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver posterior inference that automatically adapts to possible sparsity in quantile regression  ...  Our work helps to uncloak the value of Bayesian computational methods in frequentist inference for quantile regression.  ...  It is important to note that unadjusted Bayesian inference is not automatically valid since the posterior is constructed operationally from a misspecified asymmetric Laplace working likelihood.  ... 
arXiv:2111.00642v1 fatcat:7jztb7vw2vc2teln4v3gasnur4

Shaky Student Growth? A Comparison of Robust Bayesian Learning Progress Estimation Methods

Boris Forthmann, Natalie Förster, Elmar Souvignier
2022 Journal of Intelligence  
: (a) a Gaussian model, (b) a model based on Student's t-distribution (i.e., a robust model), and (c) an asymmetric Laplace model (i.e., Bayesian quantile regression and an alternative robust model).  ...  of measurement precision (i.e., for those estimates that were either associated with the lowest or highest degree of measurement precision).  ...  In addition, we added a Bayesian latent growth model based on an asymmetric Laplace model (i.e., Bayesian quantile regression) with the median as a conditional quantile to the set of candidate models.  ... 
doi:10.3390/jintelligence10010016 pmid:35324572 pmcid:PMC8949320 fatcat:zas5obegdzcbxloc7zfs6h7lyi

Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach

Surya T. Tokdar, Joseph B. Kadane
2012 Bayesian Analysis  
We introduce a semi-parametric Bayesian framework for a simultaneous analysis of linear quantile regression models.  ...  For a univariate covariate, we present a simpler equivalent characterization of the monotonicity constraint through an interpolation of two monotone curves.  ...  Acknowledgement We would like to thank the Editor, an Associate Editor and a referee whose feedback on an earlier draft of this paper has led to a much improved exposition of the material.  ... 
doi:10.1214/12-ba702 fatcat:e3vgdjhbaze4vhq3slzus6la7a

Beyond mean regression

Thomas Kneib
2013 Statistical Modelling  
-Assume an asymmetric Laplace distribution for the responses, i.e. y i ∼ ALD(η iτ , σ 2 , τ ) with density exp ( −w τ (y i , η iτ ) |y i − η iτ | σ 2 ) .  ...  -A combination with mixed model methodology allows to estimate the smoothing parameters. • Bayesian inference: -Similarly as for quantile regression, an asymmetric normal distribution can be defined as  ...  • Acknowledgements: -This talk is mostly based on joint work with Nora Fenske, Benjamin Hofner, Torsten Hothorn, Göran Kauermann, Stefan Lang, Andreas Mayr, Matthias Schmid, Linda Schulze Waltrup, Fabian  ... 
doi:10.1177/1471082x13494159 fatcat:bo4dwybemrevnl57vzzctdcv5y

Bayesian analysis of a Tobit quantile regression model

Keming Yu, Julian Stander
2007 Journal of Econometrics  
This paper develops a Bayesian framework for Tobit quantile regression.  ...  Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context.  ...  We are extremely grateful to Professor Siddhartha Chib for his extensive comments on the original manuscript. His comments were particularly helpful in comparing other methods for the models.  ... 
doi:10.1016/j.jeconom.2005.10.002 fatcat:xjbusdleu5ewhlk5cdck365hyy

Joint Quantile Regression for Spatial Data [article]

Xu Chen, Surya T. Tokdar
2019 arXiv   pre-print
A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing.  ...  An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence.  ...  , 1978, KB) , joint quantile regression model (JQR) by YT17, Bayesian quantile regression model using asymmetric Laplace error distribution by (Yu and Moyeed, 2001, ALDQR) , and, spatial quantile regression  ... 
arXiv:1910.13119v1 fatcat:jlgyav7bv5hmpmtlj2jb2o6pqq

Markov-switching quantile autoregression: a Gibbs sampling approach

Xiaochun Liu, Richard Luger
2017 Studies in Nonlinear Dynamics & Econometrics  
We also develop a Gibbs sampling approach for posterior inference by using data augmentation and a location-scale mixture representation of the asymmetric Laplace distribution.  ...  Monte Carlo experiments and an empirical application to the U.S. real interest rate show that both inference and forecasting are improved when the quantile monotonicity restriction is taken into account  ...  As Yu and Moyeed (2001) and Tsionas (2003) explain, the asymmetric Laplace distribution provides a natural pathway for the Bayesian analysis of quantile regression models.  ... 
doi:10.1515/snde-2016-0078 fatcat:nrl3vgfbqjcldgmcbx4qhmjs3q

Likelihood analysis for a class of beta mixed models

Wagner Hugo Bonat, Paulo Justiniano Ribeiro, Walmes Marques Zeviani
2014 Journal of Applied Statistics  
Beta regression models are a suitable choice for continuous response variables on the unity interval.  ...  We focus on likelihood inference and related algorithms for the analysis of beta mixed models motivated by two real problems with grouped data structures.  ...  Results for Bayesian inference (K = 1) are similar for the original and the 50 fold cloned data.  ... 
doi:10.1080/02664763.2014.947248 fatcat:kual4uqvivflbh2zzrlzuxq6o4

Page 4706 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
Inference 4 (1980), no. 2, 123-143; MR 82c:62046; Biometrical J. 24 (1982), no. 6, 613-627; MR 84f:62038] is studied from the Bayesian point of view and an accurate ap- proximation to its posterior distribution  ...  An interesting result for this case then obtains, namely, the joint posterior distribution of the regression coefficients and p is independent of vo, and has the form obtained by Zellner (1971) using i.i.d  ... 

Bayesian semiparametric additive quantile regression

Elisabeth Waldmann, Thomas Kneib, Yu Ryan Yue, Stefan Lang, Claudia Flexeder
2013 Statistical Modelling  
While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution  ...  In this paper, we utilize a location-scale mixture of normals representation of the asymmetric Laplace distribution to transfer different flexible modelling concepts from Gaussian mean regression to Bayesian  ...  We also thank Felix Heinzl for providing his code on DPMs in mean regression and Joachim Heinrich for sharing his expertise on the childhood growth study.  ... 
doi:10.1177/1471082x13480650 fatcat:gewvavnhynhopddmpujanincqa

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

Bruno Santos, Heleno Bolfarine
2015 arXiv   pre-print
In this work we show 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  ...  We build up an Markov Chain Monte Carlo method from related models in the literature to obtain samples from the posterior distribution.  ...  For a Bayesian setting, the asymmetric Laplace distribution can be useful in obtaining posterior conditional quantile estimates.  ... 
arXiv:1511.05925v1 fatcat:tpedpfsntra2fpjvmwfjww5dbq

bayesQR: A Bayesian Approach to Quantile Regression

Dries F. Benoit, Dirk Van den Poel
2017 Journal of Statistical Software  
The R package bayesQR contains a number of routines to estimate quantile regression parameters using a Bayesian approach based on the asymmetric Laplace distribution.  ...  After its introduction by Koenker and Basset (1978) , quantile regression has become an important and popular tool to investigate the conditional response distribution in regression.  ...  In this Bayesian approach to quantile regression, the error term is assumed to follow the asymmetric Laplace distribution.  ... 
doi:10.18637/jss.v076.i07 fatcat:b7ht4ycdlfdzndyeio3qcjcrai

Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data

Lane F. Burgette, Jerome P. Reiter
2013 Bayesian Analysis  
We propose an approach to modeling multinomial outcomes with many levels based on a Bayesian multinomial probit (MNP) model and a multiple shrinkage prior distribution for the regression parameters.  ...  The prior distribution encourages the MNP regression parameters to shrink toward a number of learned locations, thereby substantially reducing the dimension of the parameter space.  ...  In Scenario 1, we draw each (β 1j , β 2j ) from homoscedastic Laplace distributions, for which the lasso-type estimates coincide with Bayesian MAP estimators.  ... 
doi:10.1214/13-ba816 pmid:24358073 pmcid:PMC3863948 fatcat:wvacaa6cqve5bhm6uhs2lve25a
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