Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector $\mathbf{X}$ given the value $T(\mathbf{X})=\mathbf{t}$ for a function $T(\mathbf{X})$. Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions $\varphi (\mathbf{X})$ by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance sampling and change of variables. In the present paper we reformulate the problem by introducing an artificial parametric model in which $\mathbf{X}$ is a pivotal quantity, and next representing the conditional distribution of $\mathbf{X}$ given $T(\mathbf{X})=\mathbf{t}$ within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness-of-fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed.

中文翻译：

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重新审视有条件的蒙特卡罗

条件蒙特卡罗是指从随机向量的条件分布中采样$\mathbf{X}$给定值$吨(\mathbf{X})=\mathbf{吨}$对于一个函数$吨(\mathbf{X})$. 经典的条件蒙特卡罗方法被设计用于估计函数的条件期望$\phi (\mathbf{X})$通过从某些加权方案获得的无条件分布中采样。基本成分是使用重要性抽样和变量的变化。在本文中，我们通过引入人工参数模型来重新表述问题，其中$\mathbf{X}$是一个关键量，接下来表示的条件分布$\mathbf{X}$给定$吨(\mathbf{X})=\mathbf{吨}$在这个新模型中。该方法通过几个示例来说明，包括简短的模拟研究和对真实数据的拟合优度测试的应用。简要讨论了与基于充分统计的相关方法的联系。