Bayesian Semiparametric Median Regression Modeling

By Athanasios Kottas, Alan E. Gelfand. 2001

218 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/283ce96d3f71a1ca956e5f41e9d6a81844347cab

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Citations in the corpus

Inference for Mixtures of Finite Polya Tree Models (2006, methodology): “Data presented in Maksymiuk et al. (1994) were analyzed with median-regression models (which have the AFT property) by Ying, Jung, and Wei (1995), Walker and Mallick (1999), Yang (1999), and Kottas and Gelfand (2001) on the treatment of limited-stage small-cell lung cancer in n = 121 patients.”
Nonparametric Bayesian survival analysis using mixtures of Weibull distributions (2006, methodology): “Other representation results (Choquet-type theorems) suggest the choice of the kernel of the DP mixture when certain distributional shapes or properties are desired (see, e.g., Brunner & Lo, 1989, Brunner, 1992, and Kottas & Gelfand, 2001).”
Bayesian Semiparametric Modelling in Quantile Regression (2009, methodology): “In the special case of median regression (i.e. p=0.5), (6) reduces to the non-parametric error model in Kottas & Gelfand (2001).”
Bayesian quantile regression for longitudinal data models (2012, methodology): “Kottas and Gelfand [6] considered Bayesian semiparametric median regression modelling approach under a Dirichlet process mixture framework.”
Modeling Regression Error With a Mixture of Polya Trees (2002, methodology): “Kottas and Gelfand (2001) proposed a Dirichlet process scale mixture of unimodal parametric densities and also a Dirichlet process mixture of unimodal step-functions.”
The Nested Dirichlet Process (2008, methodology): “There are many recent Bayesian semiparametric approaches to survival analysis, including those of Kuo and Mallick (1997), Kottas and Gelfand (2001), and Hanson and Johnson (2002), to name only a few.”
Quantile regression: applications and current research areas (2003, methodology): “Alternatively, the accelerated failure time approach that models the logarithm of the survival time as a function of covariates can be employed (Yang, 1999; Kottas and Gelfand, 2001).”
Mixture Modeling for Marked Poisson Processes (2010, background): “In particular, for any non-increasing density h(·) on R+ there exists a distribution function G, with support on R+, such that h(t) ≡ h(t;G) = ∫ θ−11t∈(0,θ)dG(θ) (see, e.g., Brunner and Lo, 1989; Kottas and Gelfand, 2001).”
Bayesian quantile regression methods (2010, methodology): “Kottas and Gelfand (2001) propose median regression using nonparametric median zero distributions for the error term in a linear model.”
An MCMC approach to classical estimation (2003, unknown): “Hahn (1997), Chamberlain and Imbens (1997), Kottas and Gelfand (2001).”
Approximate Bayesian inference for quantiles (2005, methodology): “Kottas and Gelfand [10] and Gelfand and Kottas [11] proposed alternative approaches for modeling of median 0 residuals distributions using mixtures.”
Bayesian Tail Risk Interdependence Using Quantile Regression (2015, methodology): “The Bayesian quantile regression approach (see Yu and Moyeed, 2001; Kottas and Gelfand, 2001; Kottas and Krnjajic, 2009; Sriram et al., 2013) instead considers the distribution of Y | x as belonging to the Asymmetric Laplace distribution family, denoted by ALD (τ, q (x) , σ), with positive σ, whose ”
A partially collapsed Gibbs sampler for Bayesian quantile regression (2009, methodology): “…2007; Chen and Yu, 2008; Tsionas, 2003), Dirichlet process mixing based nonparametric median zero distribution for the regression model error (Kottas and Gelfand, 2001), an MCMC algorithm using Jeffreys’ (Jeffreys, 1961) substitution posterior for the median (Dunson and Taylor, 2005), the…”
Gibbs sampling methods for Bayesian quantile regression (2011, background): “From a Bayesian point of view, Walker and Mallick [6], Kottas and Gelfand [7], and Hanson and Johnson [8] considered median regression, which is a special case of quantile regression with p = 0.5, and discussed non-parametric modelling for the error distribution based on either Pólya tree or Dirichl”
A Bayesian Nonparametric Approach to Inference for Quantile Regression (2010, methodology): “The special case of median regression has been considered by Walker and Mallick (1999), Kottas and Gelfand (2001), and Hanson and Johnson (2002).”
Bayesian analysis of a Tobit quantile regression model (2007, methodology): “According to Kottas and Gelfand (2001), α > 0 is an arbitrary one-dimensional scale parameter and γ > 0 is a skewed parameter.”