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Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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.
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    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. 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".
    3. 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.

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