# Adaptive Rejection Metropolis Sampling Within Gibbs Sampling

@article{Gilks1995AdaptiveRM, title={Adaptive Rejection Metropolis Sampling Within Gibbs Sampling}, author={Walter R. Gilks and Nicky Best and K. K. C. Tan}, journal={Journal of The Royal Statistical Society Series C-applied Statistics}, year={1995}, volume={44}, pages={455-472} }

Gibbs sampling is a powerful technique for statistical inference. It involves little more than sampling from full conditional distributions, which can be both complex and computationally expensive to evaluate. Gilks and Wild have shown that in practice full conditionals are often log‐concave, and they proposed a method of adaptive rejection sampling for efficiently sampling from univariate log‐concave distributions. In this paper, to deal with non‐log‐concave full conditional distributions, we…

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## References

SHOWING 1-10 OF 23 REFERENCES

### Inference from Iterative Simulation Using Multiple Sequences

- Computer Science
- 1992

The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.

### Monte Carlo Sampling Methods Using Markov Chains and Their Applications

- Mathematics
- 1970

SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and…

### A maximum likelihood estimation method for random coefficient regression models

- Mathematics
- 1986

SUMMARY A method for estimating the distribution of the parameters of a random coefficient regression model is proposed. This distribution, accounting for interindividual variability, is assumed to…

### Adaptive Rejection Sampling for Gibbs Sampling

- Business
- 1992

SUMMARY We propose a method for rejection sampling from any univariate log-concave probability density function. The method is adaptive: as sampling proceeds, the rejection envelope and the squeezing…

### Spatial Statistics and Bayesian Computation

- Computer Science
- 1993

The early development of MCMC in Bayesian inference is traced, some recent computational progress in statistical physics is reviewed, based on the introduction of auxiliary variables, and its current and future relevance in Bayesesian applications are discussed.

### Bayesian Analysis of Linear and Non‐Linear Population Models by Using the Gibbs Sampler

- Mathematics
- 1994

Abstract : A fully Bayesian analysis of linear and nonlinear population models has previously been unavailable, as a consequence of the seeming impossibility of performing the necessary numerical…

### Sampling-Based Approaches to Calculating Marginal Densities

- Computer Science
- 1990

Abstract Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the…

### Population pharmacokinetic data and parameter estimation based on their first two statistical moments.

- BiologyDrug metabolism reviews
- 1984

From the limited evidence in this investigation it appears that the linearization per se does not significantly adversely affect the estimates, and an investigation of the effect of this linearization is reported.

### Exploring Posterior Distributions Using Markov Chains

- Mathematics
- 1992

Abstract : Several Markov chain-based methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several…

### Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

- PhysicsIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1984

The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.