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首页> 外文期刊>Statistics and computing >Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks
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Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks

机译：适用于贝叶斯社交网络的双重棘手问题的高效计算策略

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摘要

Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for doubly intractable target distributions with a focus on Bayesian exponential random graph models. Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontal and rectangular) are tested and merged with the delayed rejection (DR) strategy with the aim of reducing the variance of the resulting Markov chain Monte Carlo estimators for a given computational time. The DR is modified in order to integrate it within the approximate exchange algorithm (AEA) to avoid the computation of intractable normalising constant that appears in exponential random graph models. This gives rise to the AEA + DR: a new methodology to sample doubly intractable distributions that dominates the AEA in the Peskun ordering (Peskun Biometrika 60:607-612, 1973) leading to MCMC estimators with a smaller asymptotic variance. The Bergm package for R (Caimo and Friel J. Stat. Softw. 22:518-532, 2014) has been updated to incorporate the AEA + DR thus including the possibility of adding a higher stage proposals and different forms of adaptation.
机译：对最近出现在文献中的有力想法进行了调整和组合，以针对双倍难处理的目标分布设计改进的采样器，重点放在贝叶斯指数随机图模型上。测试了各种形式的自适应Metropolis-Hastings提议（垂直，水平和矩形），并与延迟拒绝（DR）策略合并，目的是在给定的计算时间内减少所得马尔可夫链蒙特卡罗估计的方差。修改DR以便将其集成到近似交换算法（AEA）中，以避免计算出现在指数随机图模型中的难于归一化常数。这就产生了AEA + DR：一种新的抽样方法，用于以Peskun顺序（Peskun Biometrika 60：607-612，1973）控制AEA的双重棘手分布，从而导致MCMC估计量的渐近方差较小。 R的Bergm软件包（Caimo和Friel J. Stat。Softw。22：518-532，2014）已更新为包含AEA + DR，因此可以添加更高阶段的建议和不同形式的适应。

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