Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
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DOI：
10.1080/00401706.2018.1552203
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发表时间：
2017-12
期刊：
影响因子：
2.5
通讯作者：
V. R. Joseph;Dianpeng Wang;Li Gu;Shiji Lyu;Rui Tuo
中科院分区：
文献类型：
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作者：
V. R. Joseph;Dianpeng Wang;Li Gu;Shiji Lyu;Rui Tuo
摘要：马尔可夫链蒙特卡罗（MCMC）方法需要大量的样本来近似后验分布，当估计似然或先验是昂贵的时，这可能是昂贵的。如果我们可以避免重复的样本和那些彼此接近的样本，就可以减少样本的数量。这就是准蒙特卡罗（quasi-Monte Carlo， QMC）等确定性抽样方法背后的思想。然而，现有的QMC方法是从一个均匀的超立方体中采样，这可能会错过后验分布的高概率区域，从而导致近似性差。最小能量设计（mine）是最近提出的一种确定性采样方法，它利用后验评估来获得感兴趣区域的加权空间填充设计。然而，现有的mine实现效率低下，因为它需要多次全局优化，因此需要对后验进行大量评估。在本文中，我们开发了一种有效的算法，可以产生很少的后验评估的mine样本。我们还对mine准则进行了一些改进，使其在高维上表现更好。通过校准摩擦钻井过程的实例，说明了MinED相对于MCMC和QMC的优势。
Abstract Markov chain Monte Carlo ( MCMC) methods require a large number of samples to approximate a posterior distribution, which can be costly when the likelihood or prior is expensive to evaluate. The number of samples can be reduced if we can avoid repeated samples and those that are close to each other. This is the idea behind deterministic sampling methods such as quasi-Monte Carlo (QMC). However, the existing QMC methods aim at sampling from a uniform hypercube, which can miss the high probability regions of the posterior distribution and thus the approximation can be poor. Minimum energy design (MinED) is a recently proposed deterministic sampling method, which makes use of the posterior evaluations to obtain a weighted space-filling design in the region of interest. However, the existing implementation of MinED is inefficient because it requires several global optimizations and thus numerous evaluations of the posterior. In this article, we develop an efficient algorithm that can generate MinED samples with few posterior evaluations. We also make several improvements to the MinED criterion to make it perform better in high dimensions. The advantages of MinED over MCMC and QMC are illustrated using an example of calibrating a friction drilling process.