论文标题
无废物顺序蒙特卡洛
Waste-free Sequential Monte Carlo
论文作者
论文摘要
在SMC采样器中移动颗粒的一种标准方法是应用MCMC（Markov Chain Monte Carlo）内核的几个步骤。不幸的是，目前尚不清楚需要执行多少个步骤才能获得最佳性能。另外，中间步骤的输出被丢弃，因此以某种方式浪费了。我们提出了一种新的无废物SMC算法，该算法将所有这些中间MCMC步骤的输出作为粒子。我们确定其输出是一致且渐近正常的。我们使用渐近方差的表达来开发有关如何在实践中实施算法的各种见解。我们特别开发了一种从单个算法（任何粒子估计值的渐近方差）估算的方法。通过一系列数值示例，我们从经验上表明，无废物的SMC倾向于优于标准SMC采样器，尤其是在遍及迭代中所考虑的MCMC内核减少（如回火或罕见事件问题）的情况下，尤其是在这种情况下。
A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems).
