dorsal/arxiv
View SchemaSlice Sampling
| Authors | Radford M. Neal |
|---|---|
| Categories | |
| ArXiv ID | physics/0009028 |
| URL | https://arxiv.org/abs/physics/0009028 |
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.
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"abstract": "Markov chain sampling methods that automatically adapt to characteristics of\nthe distribution being sampled can be constructed by exploiting the principle\nthat one can sample from a distribution by sampling uniformly from the region\nunder the plot of its density function. A Markov chain that converges to this\nuniform distribution can be constructed by alternating uniform sampling in the\nvertical direction with uniform sampling from the horizontal `slice\u0027 defined by\nthe current vertical position, or more generally, with some update that leaves\nthe uniform distribution over this slice invariant. Variations on such `slice\nsampling\u0027 methods are easily implemented for univariate distributions, and can\nbe used to sample from a multivariate distribution by updating each variable in\nturn. This approach is often easier to implement than Gibbs sampling, and more\nefficient than simple Metropolis updates, due to the ability of slice sampling\nto adaptively choose the magnitude of changes made. It is therefore attractive\nfor routine and automated use. Slice sampling methods that update all variables\nsimultaneously are also possible. These methods can adaptively choose the\nmagnitudes of changes made to each variable, based on the local properties of\nthe density function. More ambitiously, such methods could potentially allow\nthe sampling to adapt to dependencies between variables by constructing local\nquadratic approximations. Another approach is to improve sampling efficiency by\nsuppressing random walks. This can be done using `overrelaxed\u0027 versions of\nunivariate slice sampling procedures, or by using `reflective\u0027 multivariate\nslice sampling methods, which bounce off the edges of the slice.",
"arxiv_id": "physics/0009028",
"authors": [
"Radford M. Neal"
],
"categories": [
"physics.data-an",
"physics.comp-ph"
],
"title": "Slice Sampling",
"url": "https://arxiv.org/abs/physics/0009028"
},
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