Efficient Multivariate Initial Sequence Estimators for MCMC
针对MCMC模拟中多元初始序列估计量计算慢的问题，提出一种高效替代估计量，保持其渐近性质和有限样本优越性能，并给出并行链下的单变量与多元版本。
Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC), and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on multivariate assessment of simulation error, and many multivariate generalizations of univariate methods have been developed. The multivariate initial sequence estimator is known to exhibit superior finite-sample performance compared to its competitors. However, the multivariate initial sequence estimator can be prohibitively slow, limiting its widespread use. We provide an efficient alternative to the multivariate initial sequence estimator that inherits its asymptotic properties as well as the finite-sample superior performance. The effectiveness of the proposed estimator is shown via example implementations. Further, we also present univariate and multivariate initial sequence estimators for when parallel MCMC chains are run and demonstrate their effectiveness over a popular alternative.