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G. O. Roberts, A. Gelman and W. R. Gilks, “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms”, Annals of Applied Probability, Vol. 7, No. 1, 1997, pp. 110-120.

has been cited by the following article:

• TITLE: A Bayesian Quantile Regression Analysis of Potential Risk Factors for Violent Crimes in USA

  AUTHORS: Ming Wang, Lijun Zhang

  KEYWORDS: Bayesian Quantile Regression; Asymmetric Laplace Distribution; Improper Priors; Sensitivity; Ordinary Least Square

  JOURNAL NAME: Open Journal of Statistics, Vol.2 No.5, December 19, 2012

  ABSTRACT: Bayesian quantile regression has drawn more attention in widespread applications recently. Yu and Moyeed (2001) proposed an asymmetric Laplace distribution to provide likelihood based mechanism for Bayesian inference of quantile regression models. In this work, the primary objective is to evaluate the performance of Bayesian quantile regression compared with simple regression and quantile regression through simulation and with application to a crime dataset from 50 USA states for assessing the effect of potential risk factors on the violent crime rate. This paper also explores improper priors, and conducts sensitivity analysis on the parameter estimates. The data analysis reveals that the percent of population that are single parents always has a significant positive influence on violent crimes occurrence, and Bayesian quantile regression provides more comprehensive statistical description of this association.