## Slice sampling (2000)

Venue: | Annals of Statistics |

Citations: | 147 - 5 self |

### BibTeX

@ARTICLE{Neal00slicesampling,

author = {Radford M. Neal},

title = {Slice sampling},

journal = {Annals of Statistics},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample 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, with some update that leaves the uniform distribution over this slice invariant. Variations on such ‘slice sampling ’ methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling, and more efficient than simple Metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made. It is therefore attractive for routine and automated use. Slice sampling methods that update all variables simultaneously are also possible. These methods can adaptively choose the magnitudes of changes made to each variable, based on the local properties of the density function. More ambitiously, such methods could potentially allow the sampling to adapt to dependencies between variables by constructing local quadratic approximations. Another approach is to improve sampling efficiency by suppressing random walks. This can be done using ‘overrelaxed ’ versions of univariate slice sampling procedures, or by using ‘reflective ’ multivariate slice sampling methods, which bounce off the edges of the slice.

### Citations

1216 |
Monte Carlo sampling methods using Markov chains and their applications
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(Show Context)
Citation Context ...ing, Metropolis algorithm, overrelaxation, dynamical methods. 1 Introduction Markov chain methods such as Gibbs sampling (Gelfand and Smith 1990) and the Metropolis algorithm (Metropolis, et al 1953, =-=Hastings 1970-=-) can be used to sample from many of the complex, multivariate distributions encountered in statistics. However, to implement Gibbs sampling, one may need to devise methods for sampling from non-stand... |

740 |
Sampling-based approaches to calculating marginal densities
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(Show Context)
Citation Context ...f the slice. Keywords: Markov chain Monte Carlo, adaptive methods, Gibbs sampling, Metropolis algorithm, overrelaxation, dynamical methods. 1 Introduction Markov chain methods such as Gibbs sampling (=-=Gelfand and Smith 1990-=-) and the Metropolis algorithm (Metropolis, et al 1953, Hastings 1970) can be used to sample from many of the complex, multivariate distributions encountered in statistics. However, to implement Gibbs... |

608 | Bayesian Learning for Neural Networks
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(Show Context)
Citation Context ... but there are many models for which sampling from these conditional distributions requires the development of custom algorithms, or is infeasible in practice (eg, for multilayer perceptron networks (=-=Neal 1996-=-)). Note, however, that once methods for sampling from these conditional distributions have been found, no further tuning parameters need be set in order to produce the final Markov chain sampler. The... |

561 | Probabilistic inference using Markov chain Monte Carlo methods
- Neal
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(Show Context)
Citation Context ...alks are suppressed using the Hybrid Monte Carlo or other dynamical methods (Duane, Kennedy, Pendleton, and Roweth 1987; Horowitz 1991; Neal 1994; and for reviews from a more statistical perspective, =-=Neal 1993-=-, 1996), or by using an overrelaxation method (Adler 1981; Barone and Frigessi 1990; Green and Han 1992; Neal 1998). Dynamical and overrelaxation methods are not always easy to apply, however. Use of ... |

280 |
Adaptive rejection sampling for Gibbs Sampling
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(Show Context)
Citation Context ...eters need be set in order to produce the final Markov chain sampler. The routine use of Gibbs sampling has been assisted by the development of Adaptive Rejection Sampling (ARS) (Gilks and Wild 1992; =-=Gilks 1992-=-), which can be used to efficiently sample from any conditional distribution whose density function is log concave, given only the ability to compute some function, f i (x i ), that is proportional to... |

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146 |
WinBUGS: A Bayesian modelling framework: Concepts, structure, and extensibility
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- 2000
(Show Context)
Citation Context ...to sample for latent variables in a neural network. Slice sampling is also particularly suitable for use in automatically generated samplers, and is now used in some situations by the WinBUGS system (=-=Lunn, et al 2000). Readers-=- can try out slice sampling methods for themselves, on a variety of Bayesian models, using the "software for flexible Bayesian modeling" that is available from my web page. This software (ve... |

136 | Generalization of the Fortuin-KasteleynSwendsen-Wang representation and Monte Carlo algorithm, Phys - Edwards, Sokal - 1988 |

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49 |
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(Show Context)
Citation Context ...endleton, and Roweth 1987; Horowitz 1991; Neal 1994; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (Adler 1981; Barone and Frigessi 1990; =-=Green and Han 1992-=-; Neal 1998). Dynamical and overrelaxation methods are not always easy to apply, however. Use of Markov chain samplers that avoid random walks would be assisted by the development of methods that requ... |

41 | Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation
- Neal
- 1998
(Show Context)
Citation Context ... 1987; Horowitz 1991; Neal 1994; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (Adler 1981; Barone and Frigessi 1990; Green and Han 1992; =-=Neal 1998-=-). Dynamical and overrelaxation methods are not always easy to apply, however. Use of Markov chain samplers that avoid random walks would be assisted by the development of methods that require less sp... |

40 |
Hybrid Monte Carlo
- Duane
- 1987
(Show Context)
Citation Context ...flect' off the boundaries of the slice. Such movement with reflection can be seen as a specialization to uniform distributions of the Hamiltonian dynamics that forms the basis for Hybrid Monte Carlo (=-=Duane, et al 1987-=-). As before, suppose we wish to sample from a distribution over ! n , defined by a function f(x) that is proportional to the probability density, and which we here assume is differentiable. We must b... |

25 |
Improving stochastic relaxation for Gaussian random
- Barone, Frigessi
- 1990
(Show Context)
Citation Context ...methods (Duane, Kennedy, Pendleton, and Roweth 1987; Horowitz 1991; Neal 1994; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (Adler 1981; =-=Barone and Frigessi 1990-=-; Green and Han 1992; Neal 1998). Dynamical and overrelaxation methods are not always easy to apply, however. Use of Markov chain samplers that avoid random walks would be assisted by the development ... |

25 | Some adaptive Monte Carlo methods for Bayesian inference
- Tierney, Mira
- 1999
(Show Context)
Citation Context ...have been used very successfully for optimization problems. Adaptive slice sampling appears to be simpler than a somewhat analogous scheme proposed for the Metropolis algorithm (Mira 1998, Chapter 5; =-=Tierney and Mira 1999-=-; Green and Mira 1999). However, 2 further research will be needed to fully exploit the adaptive capabilities of multivariate slice sampling. One might instead accept that dependencies between variabl... |

23 | A (2001) Delayed rejection in reversible jump Metropolis-Hastings. Biometrika 88:1035–1053
- PJ, Mira
(Show Context)
Citation Context ...cessfully for optimization problems. Adaptive slice sampling appears to be simpler than a somewhat analogous scheme proposed for the Metropolis algorithm (Mira 1998, Chapter 5; Tierney and Mira 1999; =-=Green and Mira 1999-=-). However, 2 further research will be needed to fully exploit the adaptive capabilities of multivariate slice sampling. One might instead accept that dependencies between variables will lead to the d... |

22 | Adaptive Rejection Metropolis Sampling - Gilks, Best, et al. - 1995 |

20 |
A generalized guided Monte Carlo algorithm
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- 1991
(Show Context)
Citation Context ...). Large gains in sampling efficiency can be obtained in practice when random walks are suppressed using the Hybrid Monte Carlo or other dynamical methods (Duane, Kennedy, Pendleton, and Roweth 1987; =-=Horowitz 1991-=-; Neal 1994; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (Adler 1981; Barone and Frigessi 1990; Green and Han 1992; Neal 1998). Dynamica... |

19 | An improved acceptance procedure for the Hybrid Monte Carlo Algorithm
- Neal
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(Show Context)
Citation Context ...in sampling efficiency can be obtained in practice when random walks are suppressed using the Hybrid Monte Carlo or other dynamical methods (Duane, Kennedy, Pendleton, and Roweth 1987; Horowitz 1991; =-=Neal 1994-=-; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (Adler 1981; Barone and Frigessi 1990; Green and Han 1992; Neal 1998). Dynamical and overr... |

15 |
Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions
- Adler
- 1981
(Show Context)
Citation Context ...r dynamical methods (Duane, Kennedy, Pendleton, and Roweth 1987; Horowitz 1991; Neal 1994; and for reviews from a more statistical perspective, Neal 1993, 1996), or by using an overrelaxation method (=-=Adler 1981-=-; Barone and Frigessi 1990; Green and Han 1992; Neal 1998). Dynamical and overrelaxation methods are not always easy to apply, however. Use of Markov chain samplers that avoid random walks would be as... |

9 | Spatial Statistics and Bayesian Computation" (with discussion - Besag, Green - 1993 |

9 | Continuous sigmoidal belief networks trained using slice sampling - Frey - 1997 |

2 |
Ordering, Splicing, and Splitting Monte Carlo Markov Chains
- Mira
- 1998
(Show Context)
Citation Context ...ld be constructed, as have been used very successfully for optimization problems. Adaptive slice sampling appears to be simpler than a somewhat analogous scheme proposed for the Metropolis algorithm (=-=Mira 1998-=-, Chapter 5; Tierney and Mira 1999; Green and Mira 1999). However, 2 further research will be needed to fully exploit the adaptive capabilities of multivariate slice sampling. One might instead accept... |

1 | Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation - M - 1998 |