Bayesian forecasting and dynamic models (2nd ed.)
Bayesian forecasting and dynamic models (2nd ed.)
Generating discrete random variables in a computer
Communications of the ACM
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions
Computational Statistics & Data Analysis
Finite Elements in Analysis and Design
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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.