Slice sampling
Slice sampling
复制标题
DOI：
10.1214/aos/1056562461
复制
发表时间：
2003-06-01
影响因子：
4.5
通讯作者：
Neal, RM
中科院分区：
文献类型：
--
作者：
Neal, RM
利用分布密度函数图下区域均匀抽样的原理，可以构造出适合被抽样分布特点的马尔可夫链抽样方法。收敛到该均匀分布的马尔可夫链可以通过交替地在垂直方向上均匀采样与来自由当前垂直位置定义的水平“切片”的均匀采样来构造，或者更一般地，通过一些更新来构造该切片上的均匀分布不变的马尔可夫链。这种“切片抽样”方法对于单变量分布很容易实现，并且可以通过依次更新每个变量来从多变量分布中进行抽样。这种方法通常比Gibbs抽样更容易实现，并且比简单的Metropolis更新更有效，这是因为切片抽样能够自适应地选择所做更改的大小。因此，它对常规和自动使用很有吸引力。同时更新所有变量的切片抽样方法也是可能的。这些方法可以根据密度函数的局部性质，自适应地选择每个变量的变化量。更雄心勃勃的是，这种方法可以通过构建局部二次近似来潜在地适应变量之间的相关性。另一种方法是通过抑制随机游动来提高采样效率。对于单变量切片采样可以通过“超松弛”来完成，对于多变量切片采样可以通过从切片边缘的“反射”来完成。
Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using 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. 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 adapt to the dependencies between variables by constructing local quadratic approximations. Another approach is to improve sampling efficiency by suppressing random walks. This can be done for univariate slice sampling by "overrelaxation," and for multivariate slice sampling by "reflection" from the edges of the slice.