Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we establish a multivariate central limit theorem for any finite combination of sample means and quantiles under the assumption of a strongly mixing process, which includes the standard Monte Carlo and Markov chain Monte Carlo settings. We build on this to provide a fast algorithm for constructing hyperrectangular confidence regions having the desired simultaneous coverage probability and a convenient marginal interpretation. The methods are incorporated into standard ways of visualizing the results of Monte Carlo experiments enabling the practitioner to more easily assess the reliability of the results. We demonstrate the utility of this approach in various Monte Carlo settings including simulation studies based on independent and identically distributed samples and Bayesian analyses using Markov chain Monte Carlo sampling.

中文翻译：

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评估和可视化同步仿真误差

蒙特卡罗实验产生样本以估计给定分布的特征。然而，尽管是普遍做法，但同时估计均值和分位数却很少受到关注。在此设置中，我们在强混合过程的假设下为样本均值和分位数的任何有限组合建立了多元中心极限定理，其中包括标准蒙特卡罗和马尔可夫链蒙特卡罗设置。我们以此为基础提供了一种快速算法，用于构建具有所需同时覆盖概率和方便的边缘解释的超矩形置信区域。这些方法被纳入可视化蒙特卡罗实验结果的标准方法中，使从业者能够更容易地评估结果的可靠性。