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摘要翻译：
在设计高效的仿真算法时，常常会遇到方案分布选择不当的问题。虽然给定的仿真内核的性能可以后验地说明该内核对手头的问题有多充分，但对内核的永久在线修改会引起对结果算法有效性的担忧。虽然这个问题对于MCMC算法来说是最棘手的，但对于重要性抽样算法的等效版本可以非常精确地进行验证。我们给出了自适应混合种群Monte Carlo算法收敛的充分条件，并证明了Rao-Blackwellized版本在Kullback散度准则下渐近达到最优，而更基本的版本不能从重复更新中受益。
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英文标题：
《Convergence of adaptive mixtures of importance sampling schemes》
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作者：
R. Douc, A. Guillin, J.-M. Marin, C. P. Robert
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao--Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions do not benefit from repeated updating.
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PDF链接：
https://arxiv.org/pdf/708.0711
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