Gibbs sampling methods for Bayesian quantile regression

By Hideo Kozumi, Genya Kobayashi. 2011

529 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/91417036889f743818d6b93b4e567bb59136d485

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Citations in the corpus

Posterior Consistency of Bayesian Quantile Regression Based on the Misspecified Asymmetric Laplace Density (2013, unknown): “To facilitate a simple formulation of the MCMC scheme, we use the representation of ALD as a scaled mixture of normals (see Kozumi and Kobayashi 2011).”
A generalized class of skew distributions and associated robust quantile regression models (2014, background): “We follow, among others, Kocherginsky, He, & Mu (2005), Reich, Bondell, & Wang (2010), and Kozumi & Kobayashi (2011), by considering four error distributions as the data generating process (DGP), including the normal, mixture of normals, Student’s-t with two degrees of freedom and skew normal from…”
A quantile parametric mixed regression model for bounded response variables (2017, methodology): “[26] provided an useful stochastic representation for the ALD that facilitates the implementation of a Gibbs sampling scheme for this model.”
Bayesian Tail Risk Interdependence Using Quantile Regression (2015, unknown): “Following Kozumi and Kobayashi (2011), we instead adopt the well-known representation (see e.g. Kotz et al., 2001 and Park and Casella, 2008) of ∼ ALD (τ, 0, σ) as a location-scale mixture of Gaussian distributions: = λω + δ √ σωz, (10) where ω ∼ Exp ( σ−1 ) and z ∼ N (0, 1) are independent random…”
Bayesian Quantile Regression for Ordinal Models (2016, methodology): “Estimation Estimation of the ORII model (12), although free of the MH algorithm, cannot directly utilize Gibbs sampling since the conditional mean of zi|βp, wi involves the scale parameter σp (Kozumi and Kobayashi 2011).”
Bayesian quantile regression for longitudinal data models (2012, unknown): “Then we have the following representation [23]:”
Bayesian quantile regression for ordinal longitudinal data (2016, unknown): “Assuming that the error εij of the unobserved response lij has a SLD as in (3), we have εij = (1 − 2θ)vij + √ 2vijǫij (Kozumi and Kobayashi, 2011).”