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An efficient proposal distribution for Metropolis–Hastings using a B-splines technique

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  • Shao, Wei
  • Guo, Guangbao
  • Meng, Fanyu
  • Jia, Shuqin

Abstract

In this paper, we proposed an efficient proposal distribution in the Metropolis–Hastings algorithm using the B-spline proposal Metropolis–Hastings algorithm. This new method can be extended to high-dimensional cases, such as the B-spline proposal in Gibbs sampling and in the Hit-and-Run (BSPHR) algorithm. It improves the proposal distribution in the Metropolis–Hastings algorithm by carrying more information from the target function. The performance of BSPHR was compared with that of other Markov Chain Monte Carlo (MCMC) samplers in simulation and real data examples. Simulation results show that the new method performs significantly better than other MCMC methods.

Suggested Citation

  • Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:465-478
    DOI: 10.1016/j.csda.2012.07.014
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    References listed on IDEAS

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    1. Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    2. Petris, Giovanni, 2010. "An R Package for Dynamic Linear Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i12).
    3. Liang F. & Wong W.H., 2001. "Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 653-666, June.
    4. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
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    Cited by:

    1. Fabrizio Leisen & Roberto Casarin & David Luengo & Luca Martino, 2013. "Adaptive Sticky Generalized Metropolis," Working Papers 2013:19, Department of Economics, University of Venice "Ca' Foscari".
    2. Aur'elien Hazan, 2017. "Stock-flow consistent macroeconomic model with nonuniform distributional constraint," Papers 1708.00645, arXiv.org.

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