Slice Sampling

@article{Neal2003SliceS,
  title={Slice Sampling},
  author={Radford M. Neal},
  journal={The Annals of Statistics},
  year={2003},
  volume={31(3)},
  pages={ 705–767}
}
Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using the principle that one can ample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position, or more generally… 
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References

SHOWING 1-10 OF 60 REFERENCES
Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function
TLDR
Slice sampling is attractive in routine Markov chain Monte Carlo applications, and for use by software that automatically generates aMarkov chain sampler from a model specii-cation.
Annealed importance sampling
TLDR
It is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler, which can be seen as a generalization of a recently-proposed variant of sequential importance sampling.
On the use of auxiliary variables in Markov chain Monte Carlo sampling
TLDR
The slice sampler, a method of constructing a reversible Markov chain with a speciied invariant distribution, has a smaller second-largest eigenvalue than the corresponding independence Metropolis-Hastings algorithm.
Ordering, Slicing And Splitting Monte Carlo Markov Chains
  • A. Mira
  • Mathematics, Computer Science
  • 1998
TLDR
The second part of this work shows that it is always possible to beat the Metropolis-Hastings algorithm in terms of the Peskun ordering and introduces a more useful ordering, the covariance ordering, that allows to compare a wider class of sampling schemes.
Suppressing Random Walks in Markov Chain Monte Carlo Using Ordered Overrelaxation
TLDR
An overrelaxed Markov chain Monte Carlo algorithm based on order statistics that can be applied whenever the full conditional distributions are such that their cumulative distribution functions and inverse cumulative distribution function can be efficiently computed.
Annealing Markov chain Monte Carlo with applications to ancestral inference
TLDR
This work proposes MCMC methods distantly related to simulated annealing, which simulate realizations from a sequence of distributions, allowing the distribution being simulated to vary randomly over time.
Optimum Monte-Carlo sampling using Markov chains
SUMMARY The sampling method proposed by Metropolis et al. (1953) requires the simulation of a Markov chain with a specified 7i as its stationary distribution. Hastings (1970) outlined a general
The polar slice sampler
This paper investigates the polar slice sampler, a particular type of the Markov chain Monte Carlo algorithm known as the slice sampler. This algorithm is shown to have convergence properties which
Performance of the Gibbs, Hit-and-Run, and Metropolis Samplers
Abstract We consider the performance of three Monte Carlo Markov-chain samplers—the Gibbs sampler, which cycles through coordinate directions; the Hit-and-Run (HR and the Metropolis sampler, which
Efficiency and Convergence Properties of Slice Samplers
The slice sampler (SS) is a method of constructing a reversible Markov chain with a specified invariant distribution. Given an independence Metropolis–Hastings algorithm (IMHA) it is always possible
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