We introduce a new class of sequential Monte Carlo methods called nested sampling via sequential Monte Carlo (NS-SMC), which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows convergence results to be obtained in the setting when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood (normalizing constant) estimates are unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. We show that a minor adjustment to our adaptive NS-SMC algorithm recovers the original NS algorithm, which provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. A numerical study is conducted where the performance of NS-SMC and temperature-annealed SMC is compared on challenging problems. Code for the experiments is made available online at https://github.com/LeahPrice/SMC-NS .

翻译：我们提出了一类新的序贯蒙特卡洛方法，称为基于序贯蒙特卡洛的嵌套抽样（NS-SMC），该方法将Skilling（2006）提出的嵌套抽样方法的本质重新表述为序贯蒙特卡洛技术。这一新框架允许在使用马尔可夫链蒙特卡洛（MCMC）生成新样本的情况下获得收敛结果。另一个优势是边际似然（归一化常数）估计是无偏的。与NS不同，NS-SMC的分析不需要模拟样本相互独立这一（不现实的）假设。我们表明，对自适应NS-SMC算法进行微小调整即可恢复原始NS算法，这揭示了NS为何在典型违反其假设的情况下仍能产生准确估计的深层原因。通过数值研究，我们在具有挑战性的问题上比较了NS-SMC与温度退火SMC的性能。实验代码已在线公开，网址为https://github.com/LeahPrice/SMC-NS 。