A General Purpose Sampling Algorithm for Continuous Distributions (the t-walk)
A General Purpose Sampling Algorithm for Continuous Distributions (the t-walk)
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DOI：
10.1214/10-ba60
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发表时间：
2010-01-01
影响因子：
4.4
通讯作者：
Fox, Colin
中科院分区：
文献类型：
--
作者：
Andres Christen, J.;Fox, Colin
我们开发了一种新的通用MCMC采样器，用于任意连续分布，无需调优。我们称这个MCMC为t-walk。t-walk在样本空间中保持两个独立的点，所有的移动都基于提案，然后在产品空间上以标准的Metropolis-Hastings接受概率被接受。因此，t-walk在通常的温和条件下是收敛的。我们将建议分布或“移动”限制为那些产生对比例不变的算法，并且对状态空间的仿射变换近似不变的算法。因此，可能用于提高采样器效率的提案缩放和垂直坐标变换都不需要，因为t-walk的操作在目标分布的任何缩放版本上都是相同的。给出了四种可实现垂直采样算法的方法。我们使用简单的装置，在每一步只更新一个随机的坐标子集，以允许将t-walk应用于高维问题。在一系列跨维度的测试问题中，我们发现t-walk的效率只比优化算法低一个小因素，但明显优于一般的随机漫步M-H采样器，这些随机漫步M-H采样器没有针对特定问题进行优化。此外，对于不存在最优仿射变换的目标分布，例如在状态空间的不同区域中相关结构非常不同的目标分布，t-walk仍然是直立的。给出了几个例子，显示了良好的混合和收敛特性，从1到200不等的尺寸，具有完全不同的尺度和相关结构，使用完全相同的采样器。t-walk可用于R、Python、Lab和c++，网址为http://www.cimat.mx/similar to jac/ walk/。
We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. We call this MCMC the t-walk. The t-walk maintains two independent points in the sample space, and all moves are based on proposals that are then accepted with a standard Metropolis-Hastings acceptance probability on the product space. Hence the t-walk is provably convergent under the usual mild requirements. We restrict proposal distributions, or 'moves', to those that produce analgorithm that is invariant to scale, and approximately invariant to affine transformations of the state space. Hence scaling of proposals, and erectively also coordinate transformations, that might be used to increase efficiency of the sampler, are not needed since the t-walk's operation is identical on any scaled version of the target distribution. Four moves are given that result in an erective sampling algorithm.We use the simple device of up dating only a random subset of coordinates at each step to allow application of the t-walk to high-dimensional problems. In a series of test problems across dimensions we find that the t-walk is only a small factor lesse efficient than optimally tuned algorithms, but significantly outperforms general random-walk M-H samplers that are not tuned for specific problems. Further, thet-walk remains erective for target distributions for which no optimal affine transformation exists such as those where correlation structure is very different in differing regions of state space.Several examples are presented showing good mixing and convergence characteristics, varying in dimensions from 1 to 200 and with radically different scale and correlation structure, using exactly the same sampler. The t-walk is available for R, Python, at Lab and C++ at http://www.cimat.mx/similar to jac/twalk/.