MCMC收敛判据：Gelman-Rubin检验和自相关时间

最新推荐文章于 2024-11-15 14:02:44 发布

Xianyu_Wang

最新推荐文章于 2024-11-15 14:02:44 发布

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本文介绍了MCMC（Markov Chain Monte Carlo）方法中评估收敛性的两种关键指标：Gelman-Rubin统计量和自相关时间。Gelman-Rubin统计量通过比较链的平均中位数与中位数的平均来衡量链之间的相似性，当接近1时表明链已收敛。Tz检验则关注独立抽样的数量，以确定参数分布的精度。自相关时间则指示了链需要多少步才能忘记初始位置，从而影响MCMC运行的误差。

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MCMC收敛判据：Gelman-Rubin检验和自相关时间

Gelman-Rubin 检验

The Gelman Rubin Statistic compares the mean of medians vs the median of means of the chains. It is essentially a measure of how similar the chains are and asymptotically approaches 1 as they become identical. The more similar they are, the more likely they each represent the true, underlying posterior. All parameters must each have a Gelman Rubin statistic less than MAXGR (default is 1.01) to be considered “well-mixed” or “converged”.