Modeling Regression Error With a Mixture of Polya Trees

By Timothy E. Hanson, Wesley O. Johnson. 2002

234 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bc0d7a1df16b78d7f0609a07f51568ddf1f56a0c

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Citations in the corpus

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). This work is based on a parametric form for the median regression function and nonparametric modeling for the error distribution, using either Pólya tree ”
Bayesian Semiparametric Regression for Median Residual Life (2003, unknown): “For median regression modelling, there is only the work of Kottas & Gelfand (2001), summarized below, as well as that of Walker & Mallick (1999), using a Pólya tree prior, and Hanson & Johnson (2002), using a mixture of Pólya trees prior.”
Robustifying Generalized Linear Mixed Models Using a New Class of Mixtures of Multivariate Polya Trees (2009, background): “By considering different values of c, Hanson and Johnson (2002) found the family ρ(c, j) = cj2 to be sufficiently rich to capture interesting features of the distributions under consideration.”
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”
Two-sample Bayesian Nonparametric Hypothesis Testing (2009, methodology): “This is a well known phenomena of Polya Tree priors and some interesting directions to mitigate its effects can be found in Hanson and Johnson [2002], Paddock et al. [2003], Hanson [2006]. To this aim we also provided an automated empirical Bayes procedure which centres the partition on the empirica”
Approximate Bayesian inference for quantiles (2005, methodology): “Hanson and Johnson [9] generalized this approach to smooth out the partitioning effect by using a mixture of Polya trees.”
Inference for Mixtures of Finite Polya Tree Models (2006, methodology): “Furthermore, the mixture aspect of an MPT smooths out partitioning effects inherent in a simple PT (Sec. 2.1; see also Lavine 1992; Hanson and Johnson 2002).”
Bayesian Semiparametric Median Regression Modeling (2001, methodology): “…Association December 2001, Vol. 96, No. 456, Theory and Methods 1458 only of the approach of Walker and Mallick (1999), described also by Walker et al. (1999), which uses a Pólya tree prior, and the very recent work of Hanson and Johnson (2001), which uses a mixture of Pólya tree priors.”
Bayesian Nonparametrics: Models beyond the Dirichlet process (2009, unknown): “Mixtures of Pólya trees are also used in Hanson and Johnson (2002) to model the regression error and the authors investigate applications to semiparametric accelerated failure time models.”
Bayesian Semiparametric Modelling in Quantile Regression (2009, methodology): “More recently, there has been some Bayesian work on censored median regression (e.g. Walker & Mallick, 1999; Kottas & Gelfand, 2001; Hanson & Johnson, 2002), and median residual life regression (Gelfand & Kottas, 2003).”
Estimation of the density of regression errors (2005, background): “For parametric settings, there exists a recently created Bayesian theory of estimation, and for nonparametric settings, a theory of consistent estimation is developed; the interested reader can find a discussion and further references in [8] and [27].”