We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via sequential Monte Carlo (NS-SMC) and adaptive nested sampling via sequential Monte Carlo (ANS-SMC). The 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 (normalising constant) estimates given by NS-SMC are unbiased. In contrast to NS, the analysis of our proposed algorithms does not require the (unrealistic) assumption that the simulated samples be independent. We show that a minor adjustment to our ANS-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 the proposed algorithms 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，其将Skilling（2006）嵌套采样方法的核心思想用序贯蒙特卡洛技术重新表述。本文提出了两种新算法：基于序贯蒙特卡洛的嵌套采样（NS-SMC）和基于序贯蒙特卡洛的自适应嵌套采样（ANS-SMC）。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性结果。另一个优点是NS-SMC提供的边缘似然（归一化常数）估计是无偏的。与NS相比，对我们所提算法的分析不需要（不切实际的）模拟样本相互独立的假设。我们证明，对ANS-SMC算法进行微调即可恢复原始NS算法，这为理解为何NS在其假设通常被违反的情况下似乎仍能产生准确估计提供了启示。我们进行了数值研究，在具有挑战性的问题上比较了所提算法与退火温度SMC的性能。实验代码已在https://github.com/LeahPrice/SMC-NS 在线发布。