This invited feature article introduces and provides an extensive simulation study of a new Approximate Bayesian Computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, which unifies and extends previous ABC method. This framework, copulaABcdrf, aims to accurately estimate and describe the possibly skewed and high dimensional posterior distribution by a novel multivariate copula-based meta-\textit{t} distribution, based on univariate marginal posterior distributions which can be accurately estimated by Distribution Random Forests (drf), while performing automatic summary statistics (covariates) selection, and robust estimation of copula dependence parameters. The copulaABcdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation, and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of copulaABcdrf is illustrated and compared to standard ABC methods, through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. We also study a new solution to the simulation cost problem in ABC. The copulaABcdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks. The results of the simulation and empirical studies, and their implications for future research, are summarized. Keywords: Bayesian analysis, Maximum Likelihood, Intractable likelihood.

翻译：这篇特邀专题文章介绍了一种新的近似贝叶斯计算（ABC）框架——copulaABcdrf，用于估计由难处理似然定义的模型参数的后验分布和最大似然估计（MLE），该框架统一并扩展了先前的ABC方法。本文通过大量模拟研究对该框架进行了深入分析。copulaABcdrf框架旨在通过一种新颖的基于多元Copula的元t分布来精确估计并描述可能具有偏态和高维特性的后验分布，该分布建立在可由分布随机森林（drf）精确估计的单元边际后验分布基础上，同时执行自动摘要统计量（协变量）选择以及Copula依赖参数的稳健估计。该框架还提供了一种新颖的多元众数估计器用于执行MLE和后验众数估计，并包含一个可选步骤，可通过drf估计的后验概率从给定模型集中进行模型选择。通过多项模拟研究，我们展示并比较了copulaABcdrf与标准ABC方法在后验分布估计精度上的表现，这些研究涉及具有可计算后验分布的低维与高维模型（包括单峰、偏态或多峰分布），以及指数随机图模型和机制网络模型——这两类模型均定义于难以处理的似然函数，且模拟大规模网络数据集的成本高昂。我们还针对ABC中的模拟成本问题提出了一种新的解决方案。通过分析大规模现实网络数据，进一步阐释了copulaABcdrf框架与标准ABC方法的应用。本文总结了模拟与实证研究的结果及其对未来研究的启示。关键词：贝叶斯分析，最大似然，难处理似然。