Unbiased and consistent nested sampling via sequential Monte Carlo
Unbiased and consistent nested sampling via sequential Monte Carlo
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发表时间：
2018-05
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通讯作者：
R. Salomone;Leah F. South;A. M. Johansen;C. Drovandi;Dirk P. Kroese
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作者：
R. Salomone;Leah F. South;A. M. Johansen;C. Drovandi;Dirk P. Kroese
我们引入了一类新的顺序蒙特卡罗方法，称为通过顺序蒙特卡罗嵌套采样 (NS-SMC)，它根据顺序蒙特卡罗技术重新构建了 Skilling (2006) 的嵌套采样方法。当使用马尔可夫链蒙特卡罗 (MCMC) 生成新样本时，这一新框架允许人们获得边际似然和后验推断的可证明一致的估计。另一个好处是边际可能性估计也是无偏的。与 NS 相比，NS-SMC 的分析不需要模拟样本是独立的（不切实际的）假设。由于原始 NS 算法是 NS-SMC 的特例，因此这提供了关于为什么 NS 似乎能产生准确估计的见解，尽管通常违反了其假设。对于 NS-SMC 的应用，我们提供了通过初步试运行以自动方式调整 MCMC 内核的建议，并提出了一种在每次迭代时适当选择 MCMC 重复次数的新方法。最后，进行了数值研究，在几个具有挑战性和现实的问题上比较了 NS-SMC 和温度退火 SMC 的性能。我们的实验的 Matlab 代码可从 http://github.com/LeahPrice/SMC-NS 获取。
We introduce a new class of sequential Monte Carlo methods called Nested Sampling via Sequential Monte Carlo (NS-SMC), which reframes the Nested Sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows one to obtain provably consistent estimates of marginal likelihood and posterior inferences when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are also unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. As the original NS algorithm is a special case of NS-SMC, this provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. For applications of NS-SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. Finally, a numerical study is conducted where the performance of NS--SMC and temperature--annealed SMC is compared on several challenging and realistic problems. Matlab code for our experiments is made available at http://github.com/LeahPrice/SMC-NS .