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摘要翻译：
模拟回火(ST)是一种从多模态密度$\pi(\theta)$中采样的马尔可夫链蒙特卡罗(MCMC)方法。通常，ST涉及引入一个辅助变量$k$在$[0,1]$的有限子集中取值，并索引一组简化分布，例如$\pi_k(\theta)\propto\pi(\theta)^k$。在本例中，$k$的小值可以促进更好的混合，但是只有当$(\theta,k)$的联合链达到$k=1$时，才能获得来自$\pi$的样本。但是，如果计算了重要性抽样(IS)权重，整个链可以用来估计感兴趣函数的$\pi$下的期望。不幸的是，这种方法，我们称之为重要性缓和(IT)，可能会让人失望。这部分是因为最明显的实现是NA\“IVE,它可以导致高方差估计量。我们导出了一种新的组合多个is估计量的最优方法，并证明了所得到的估计量具有与有效样本量有关的高度理想的性质。我们简要地报告了在两个需要可逆跳变MCMC的建模场景中最优组合的成功，而NA\”IVE方法失败了。
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英文标题：
《Importance Tempering》
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作者：
Robert B. Gramacy, Richard J. Samworth, Ruth King
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最新提交年份：
2008
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分类信息：
一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $\pi(\theta)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$ and indexing a set of tempered distributions, say $\pi_k(\theta) \propto \pi(\theta)^k$. In this case, small values of $k$ encourage better mixing, but samples from $\pi$ are only obtained when the joint chain for $(\theta,k)$ reaches $k=1$. However, the entire chain can be used to estimate expectations under $\pi$ of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), can disappoint. This is partly because the most immediately obvious implementation is na\"ive and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that the resulting estimator has a highly desirable property related to the notion of effective sample size. We briefly report on the success of the optimal combination in two modelling scenarios requiring reversible-jump MCMC, where the na\"ive approach fails.
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PDF链接：
https://arxiv.org/pdf/707.4242
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