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## Model-based approaches to nonparametric Bayesian quantile regression

Citations: | 1 - 1 self |

### Citations

1208 | A bayesian analysis of some nonparametric problems. The annals of statistics - Ferguson - 1973 |

979 | Quantile regression
- Koenker
- 2005
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Citation Context ...rs, which are typically assumed independent from a distribution (with density, say, fp(·)) that has p-th quantile equal to 0. (See, e.g., the review paper by Yu, Lu and Stander, 2003, and the book by =-=Koenker, 2005-=-.) This literature is dominated by semiparametric techniques where the error density fp(·) is left unspecified (apart from the restriction ∫ 0 −∞ fp(ɛ)dɛ = p). Hence, since there is no probability mod... |

651 | Bayesian density estimation and inference using mixtures,” - Escobar, West - 1995 |

642 |
Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics,
- Antoniak
- 1974
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Citation Context ... in realizations G that are closer to G0. We will write G ∼ DP(α, G0) to indicate that a DP prior is used for the random distribution G. In fact, DP-based modeling typically utilizes mixtures of DPs (=-=Antoniak 1974-=-), i.e., ind yi | δi1, δi2, σ1i, σ2i ∼ kp(yi − δi1 − δi2; σ1i, σ2i) (δ1ℓ, ..., δnℓ) | τ 2 ind ℓ , φℓ ∼ Nn(0, Sℓ(τ 2 ℓ , φℓ)) ind (σr1, ..., σrn) | αr, dr ∼ p(σr1, ..., σrn | αr, dr), (5) a more genera... |

628 | Markov chain sampling methods for Dirichlet process mixture models - Neal |

571 |
A constructive definition of Dirichlet priors.
- SETHURAMAN
- 1994
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Citation Context ...) a more general version of the DP prior that involves hyperpriors for α and/or the parameters of G0. The most commonly used DP definition is its constructive definition (Sethuraman and Tiwari, 1982; =-=Sethuraman, 1994-=-), which characterizes DP realizations as countable mixtures of point masses (and thus as random discrete distributions). Specifically, a random distribution G generated from DP(α, G0) is (almost sure... |

441 |
Ferguson distributions via Polya urn schemes. The Annals of Statistics,
- Blackwell, MacQueen
- 1973
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Citation Context ...at involves the normal finite dimensional distributions for the hℓ(xiℓ) induced by the GP priors, and the priors for the σri induced by marginalizing the random distributions Gr over their DP priors (=-=Blackwell and MacQueen, 1973-=-). Let δi1 = h1(xi1) and represented in terms of successive complete conditionals, with σr1 ∼ Gr0, and for each i = 2, ..., n, p(σri | σr1, ..., σr,i−1, αr, dr) given by a mixed distribution with poin... |

388 | Gibbs sampling methods for stick-breaking priors.
- Ishwaran, James
- 2001
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Citation Context ...involves direct approximation of G in model (7), using the constructive definition of its DP(α, G0) prior, and then application of an MCMC technique for the induced discrete mixture model (see, e.g., =-=Ishwaran and James, 2001-=-). Results from comparison of this method with the approach of Section 3.2 will be reported elsewhere. Regarding the approach of Section 2, we note that there has been relatively limited work in the B... |

252 |
Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion
- Silverman
- 1985
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Citation Context ...anel, the black line denotes the posterior mean and the blue lines contain a 90% posterior interval. 3.3 Data example We illustrate the methodology of Section 3.2 with the motorcycle data (see, e.g., =-=Silverman, 1985-=-), which consist of 133 measurements of velocity in time for the helmet of a motorcycle crash victim after impact. (The data set is available from the MASS package for R.) Note that model (6) incorpor... |

150 | Monte Carlo implementation of Gaussian Process models for Bayesian regression and classification.
- Neal
- 1997
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Citation Context ...ble nonparametric prior models for the quantile regression function and the random error density. In particular, we work with independent Gaussian process (GP) priors for h1(·) and h2(·). (See, e.g., =-=Neal, 1997-=-, 1998, on GP regression under parametric error distributions.) To avoid identifiability issues, we set the GP mean functions to zero, E(hℓ(x)) = 0, for all x. We have also observed empirically that a... |

135 | A semiparametric Bayesian model for randomised block designs. - Bush, MacEachern - 1996 |

128 | Quantile smoothing splines. - Koenker, Pin, et al. - 1994 |

119 |
Nonparametric Bayesian data analysis.
- Muller, Quintana
- 2004
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Citation Context ...is based on a parametric form for the median regression function and nonparametric modeling for the error distribution, using either Pólya tree priors or Dirichlet process mixture priors. (See, e.g., =-=Müller and Quintana, 2004-=-, for reviews of these nonparametric prior models.) Regarding quantile regression, based again on parametric regression functions, Yu and Moyeed (2001) and Tsionas (2003) discuss parametric inference ... |

109 | Regression and classification using Gaussian process priors - Neal - 1998 |

84 | Bayesian curve fitting using multivariate normal mixtures. - Muller, Erkanli, et al. - 1996 |

39 | A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models.
- Gelfand, Kottas
- 2002
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Citation Context ...G|θ, α, ψ). The latter requires simulation from the DP with parameters given above, which we implement using the DP constructive definition (discussed in Section 2.1) with a truncation approximation (=-=Gelfand and Kottas, 2002-=-; Kottas, 2006). Therefore, this approach yields samples {Gb, θb, αb, ψb : b = 1, ..., B} from the full posterior (8). Each posterior realization Gb is a discrete distribution with point masses at ϑrb... |

38 |
Convergence of Dirichlet Measures and the Interpretation of their Parameter
- Sethuraman, Tiwari
- 1982
(Show Context)
Citation Context ...p(σr1, ..., σrn | αr, dr), (5) a more general version of the DP prior that involves hyperpriors for α and/or the parameters of G0. The most commonly used DP definition is its constructive definition (=-=Sethuraman and Tiwari, 1982-=-; Sethuraman, 1994), which characterizes DP realizations as countable mixtures of point masses (and thus as random discrete distributions). Specifically, a random distribution G generated from DP(α, G... |

36 | Bayesian quantile regression. - Yu, Moyeed - 2001 |

34 | Modeling Regression Error With a Mixture of Polya Trees, - Hanson, Johnson - 2002 |

34 | Bayesian semiparametric median regression modeling. - Kottas, Gelfand - 2001 |

30 |
Nonparametric Estimation of an Additive Quantile Regression Model
- Horowitz, Lee
- 2005
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Citation Context ...ents or resampling methods. The classical literature includes also work that relaxes the parametric (linear) regression form for the quantile regression function (see, e.g., He, Ng and Portnoy, 1998; =-=Horowitz and Lee, 2005-=-). By comparison with the existing volume of classical work, the Bayesian literature on quantile regression is relatively limited. The special case of median regression has been considered in Walker a... |

24 | A nonparametric Bayes method for isotonic regression - Lavine, Mockus - 1995 |

20 | Approximate Bayesian inference for quantiles
- Dunson, Taylor
- 2005
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Citation Context ...less of the estimation method (likelihood or Bayesian). There are certain approaches that allow, in the context of this framework, simultaneous estimation for more than one quantile regression (e.g., =-=Dunson & Taylor, 2005-=-); however, this is only possible because they do not involve modeling for the errors, but are rather based on approximate methods (e.g., certain pseudo-likelihoods). Hence, the additive quantile regr... |

19 | Bayesian quantile inference - Tsionas - 2003 |

17 | Bayes methods for a symmetric unimodal density and its mode - Brunner, Lo - 1989 |

17 | A Bayesian semiparametric accelerated failure time model - WALKER, MALLICK - 1999 |

14 | Bayesian linear regression with error terms that have symmetric unimodal densities - Brunner - 1995 |

13 |
Nonparametric Bayesian survival analysis using mixtures of Weibull distributions
- Kottas
(Show Context)
Citation Context ...uires simulation from the DP with parameters given above, which we implement using the DP constructive definition (discussed in Section 2.1) with a truncation approximation (Gelfand and Kottas, 2002; =-=Kottas, 2006-=-). Therefore, this approach yields samples {Gb, θb, αb, ψb : b = 1, ..., B} from the full posterior (8). Each posterior realization Gb is a discrete distribution with point masses at ϑrb = (˜µ rb , ˜ ... |

13 | Bayesian nonparametric modeling in quantile regression - Kottas, Krnjajić - 2009 |

10 | Bayesian growth curves using normal mixtures with nonparametric weights - Scaccia, Green - 2003 |

7 | Nonparametric quantile inference using Dirichlet processes - Hjort, Petrone - 2007 |

5 | Quantile regression using the RJMCMC algorithm - Yu - 2002 |

1 | Quantile regression using RJMCMC algorithm - unknown authors - 2002 |