On particle Gibbs sampling
On particle Gibbs sampling
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DOI：
10.3150/14-bej629
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发表时间：
2015-08-01
期刊：
影响因子：
1.5
通讯作者：
Singh, Sumeetpal S.
中科院分区：
文献类型：
--
作者：
Chopin, Nicolas;Singh, Sumeetpal S.
粒子吉布斯采样器是一种马尔可夫链蒙特卡罗 (MCMC) 算法，用于从状态空间模型的完整后验分布中进行采样。它通过在由相互作用的粒子系统生成的辅助变量的空间上定义的扩展目标分布上执行吉布斯采样步骤来实现这一点。本文对该算法的理论研究做出以下贡献。首先，我们提出了来自不同起点的两个粒子吉布斯更新之间的耦合结构，并表明通过增加粒子数量可以使耦合概率任意接近于 1。我们得到的直接推论是粒子吉布斯核是一致遍历的。其次，我们展示了如何包含一个额外的吉布斯采样步骤来重新选择粒子吉布斯扩展目标分布的祖先，这是实践中改进混合的流行方法，确实产生了理论上更有效的算法（通过渐近方差来衡量）。第三，我们扩展粒子吉布斯以使用较低方差的重采样方案。提供了详细的数值研究来证明粒子吉布斯和所提出的变体的效率。
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the space of the auxiliary variables generated by an interacting particle system. This paper makes the following contributions to the theoretical study of this algorithm. Firstly, we present a coupling construction between two particle Gibbs updates from different starting points and we show that the coupling probability may be made arbitrarily close to one by increasing the number of particles. We obtain as a direct corollary that the particle Gibbs kernel is uniformly ergodic. Secondly, we show how the inclusion of an additional Gibbs sampling step that reselects the ancestors of the particle Gibbs' extended target distribution, which is a popular approach in practice to improve mixing, does indeed yield a theoretically more efficient algorithm as measured by the asymptotic variance. Thirdly, we extend particle Gibbs to work with lower variance resampling schemes. A detailed numerical study is provided to demonstrate the efficiency of particle Gibbs and the proposed variants.