ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION
ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION
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DOI：
10.1088/0067-0049/213/1/14
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发表时间：
2014-07
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影响因子：
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通讯作者：
B. Liu
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作者：
B. Liu
我们描述了一种算法，可以自适应地提供多模态后验分布的混合摘要。所涉及的后验参数空间大小从几个维度到几十个维度不等。这项工作的动机是一个叫做系外行星探测的天体物理问题，其中贝叶斯模型比较所需的随机积分的计算是具有挑战性的。难点在于高度非线性的模型会导致多模态后验分布。我们采用重要性抽样（IS）来估计积分，从而将问题转化为如何找到后验的参数近似值。为了捕获后验中的多模态结构，我们初始化一个混合建议分布，然后精心定制其参数，使其尽可能与后验相似。我们使用基于IS绘制计算的有效样本量（ESS）来衡量近似程度。ESS越大，建议越接近后验。这种裁剪操作中的一个困难在于调整混合方案中混合组分的数量。蛮力方法只是将其预设为一个大常数，这会导致所需计算资源的增加。我们提供了一个迭代的删除/合并/添加过程，它与期望最大化步骤协同工作，以在线定制这样的数字。通过模拟研究和实际系外行星数据分析，验证了该方法的有效性。
We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation–maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.