Despite their popularity and flexibility, questions remain regarding how to optimally solve particular unknown variables of interest using Monte Carlo simulation experiments. This article reviews two common approaches based on either performing deterministic iterative searches with noisy objective functions or by constructing interpolation estimates given fitted surrogate functions, highlighting the inefficiencies and inferential concerns of both methods. To address these limitations, and to fill a gap in existing Monte Carlo experimental methodology, a novel algorithm termed the probabilistic bisection algorithm with bolstering and interpolations (ProBABLI) is presented with the goal providing efficient, consistent, and unbiased estimates (with associated confidence intervals) for the stochastic root equations found in Monte Carlo simulation research. Properties of the ProBABLI approach are demonstrated using practical sample size planning applications for independent samples t tests and structural equation models given target power rates, precision criteria, and expected power functions that incorporate prior beliefs. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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通过蒙特卡罗模拟实验求解变量：随机根求解方法。


尽管它们很受欢迎且具有灵活性，但如何使用蒙特卡罗模拟实验最优地解决感兴趣的特定未知变量仍然存在问题。本文回顾了两种常见的方法，基于使用噪声目标函数执行确定性迭代搜索或通过给定拟合代理函数构建插值估计，强调了两种方法的低效率和推理问题。为了解决这些局限性，并填补现有蒙特卡罗实验方法的空白，提出了一种称为支持和插值的概率二分算法（ProBABLI）的新颖算法，其目标是提供高效、一致和无偏的估计（具有相关的置信区间） ）用于蒙特卡罗模拟研究中发现的随机根方程。 ProBABLI 方法的属性通过独立样本 t 检验的实际样本量规划应用程序和给定目标功率率、精度标准和包含先验信念的预期功率函数的结构方程模型来演示。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。