IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i7p3408-3423.html
   My bibliography  Save this article

Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2

Author

Listed:
  • Meyer, Renate
  • Cai, Bo
  • Perron, François

Abstract

A crucial problem in Bayesian posterior computation is efficient sampling from a univariate distribution, e.g. a full conditional distribution in applications of the Gibbs sampler. This full conditional distribution is usually non-conjugate, algebraically complex and computationally expensive to evaluate. We propose an alternative algorithm, called ARMS2, to the widely used adaptive rejection sampling technique ARS [Gilks, W.R., Wild, P., 1992. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41 (2), 337-348; Gilks, W.R., 1992. Derivative-free adaptive rejection sampling for Gibbs sampling. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Clarendon, Oxford, pp. 641-649] for generating a sample from univariate log-concave densities. Whereas ARS is based on sampling from piecewise exponentials, the new algorithm uses truncated normal distributions and makes use of a clever auxiliary variable technique [Damien, P., Walker, S.G., 2001. Sampling truncated normal, beta, and gamma densities. Journal of Computational and Graphical Statistics 10 (2) 206-215]. Furthermore, we extend this algorithm to deal with non-log-concave densities to provide an enhanced alternative to adaptive rejection Metropolis sampling, ARMS [Gilks, W.R., Best, N.G., Tan, K.K.C., 1995. Adaptive rejection Metropolis sampling within Gibbs sampling. Applied Statistics 44, 455-472]. The performance of ARMS and ARMS2 is compared in simulations of standard univariate distributions as well as in Gibbs sampling of a Bayesian hierarchical state-space model used for fisheries stock assessment.

Suggested Citation

  • Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3408-3423
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00008-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Antonietta Mira & Luke Tierney, 2002. "Efficiency and Convergence Properties of Slice Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 1-12, March.
    2. 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.
    3. Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
    4. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    2. Cai, Bo & Meyer, Renate, 2011. "Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1260-1272, March.
    3. 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".

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
    2. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    3. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    4. Hazan, Alon & Landsman, Zinoviy & E Makov, Udi, 2003. "Robustness via a mixture of exponential power distributions," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 111-121, February.
    5. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
    6. Xiao Li & Michele Guindani & Chaan S. Ng & Brian P. Hobbs, 2021. "A Bayesian nonparametric model for textural pattern heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 459-480, March.
    7. Jelena Nikolić & Danijela Aleksić & Zoran Perić & Milan Dinčić, 2021. "Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. Chunling Wang & Xiaoyan Lin, 2022. "Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data," Stats, MDPI, vol. 5(2), pages 1-17, May.
    10. White, Gentry & Porter, Michael D., 2014. "GPU accelerated MCMC for modeling terrorist activity," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 643-651.
    11. Neville Francis & Laura E. Jackson & Michael T. Owyang, 2018. "Countercyclical Policy and the Speed of Recovery after Recessions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(4), pages 675-704, June.
    12. Helio Migon & Alexandra Schmidt & Romy Ravines & João Pereira, 2013. "An efficient sampling scheme for dynamic generalized models," Computational Statistics, Springer, vol. 28(5), pages 2267-2293, October.
    13. Cai, Bo & Lin, Xiaoyan & Wang, Lianming, 2011. "Bayesian proportional hazards model for current status data with monotone splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2644-2651, September.
    14. Huaiye Zhang & Inyoung Kim, 2016. "Adaptive Rejection Metropolis Simulated Annealing for Detecting Global Maximum Regions," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 1-19, March.
    15. Mazucheli, Josmar & Louzada-Neto, Francisco & Achcar, Jorge A., 2001. "Bayesian inference for polyhazard models in the presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 1-14, November.
    16. Pan, Chun & Cai, Bo & Wang, Lianming & Lin, Xiaoyan, 2014. "Bayesian semiparametric model for spatially correlated interval-censored survival data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 198-208.
    17. Yi-Ping Chang & Chih-Tun Yu, 2014. "Bayesian confidence intervals for probability of default and asset correlation of portfolio credit risk," Computational Statistics, Springer, vol. 29(1), pages 331-361, February.
    18. Hsieh, Ping-Hung & Yang, J. Jimmy, 2009. "A censored stochastic volatility approach to the estimation of price limit moves," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 337-351, March.
    19. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    20. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3408-3423. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.