Unbiased and consistent nested sampling via sequential Monte Carlo
通过序贯蒙特卡洛实现无偏且一致的嵌套采样AI 解读 ↓
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通过序贯蒙特卡洛实现无偏且一致的嵌套采样
- 研究问题
- 当嵌套采样通过MCMC生成相互依赖的样本时，如何建立收敛理论，并获得具有无偏性的边际似然估计？
- 方法与思路
- 作者以序贯蒙特卡洛重述嵌套采样，提出NS-SMC与自适应ANS-SMC，并讨论后者与原始嵌套采样的联系。
- 材料陈述的贡献
- 摘要称新框架允许在MCMC采样下获得收敛结果，NS-SMC的边际似然估计无偏，分析无需样本独立假设。
- 阅读关注点
- 应核对两种算法各自的收敛条件、无偏性对应的估计量，以及恢复原算法的调整和与温度退火SMC比较的设置。
- 阅读边界
- 仅据所给Crossref摘要，不能判断无偏性是否适用于所有自适应变体；收敛条件与数值比较结果未具体说明。
原文摘要
Abstract We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling (NS) method of Skilling 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 (normalizing 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.