基于分布随机森林的Copula近似贝叶斯计算
Copula Approximate Bayesian Computation Using Distribution Random Forests
AI总结：
该研究提出名为copulaABcdrf的新型近似贝叶斯计算框架，结合分布随机森林与多元copula元t分布估计后验分布，兼具变量选择、模型选择等功能，在多类模拟与真实网络数据上表现优于标准ABC方法，还可缓解模拟成本问题。
摘要：
这篇特邀专题文章介绍了一种新的近似贝叶斯计算（Approximate Bayesian Computation，ABC）框架，并对其开展了广泛的模拟研究，该框架用于估计由难解似然定义的模型参数的后验分布与最大似然估计（Maximum Likelihood Estimate，MLE），统一并拓展了已有的ABC方法。该框架名为copulaABcdrf，其核心思路是：以可通过分布随机森林（Distribution Random Forests，drf）精准估计的单变量边缘后验分布为基础，借助一种新颖的基于多元copula的元t分布，精准估计并刻画可能存在偏态的高维后验分布，同时实现摘要统计量（协变量）的自动选择，以及copula依赖参数的鲁棒估计。copulaABcdrf框架还提供了一种新颖的多元众数估计器，用于执行MLE与后验众数估计；此外还包含一个可选步骤，可利用drf估计的后验概率，从给定的模型集合中完成模型选择。研究通过多项模拟实验，验证了copulaABcdrf的后验分布估计精度，并将其与标准ABC方法进行对比：模拟实验涵盖后验分布可计算的低维与高维模型，这些模型的后验分布包括单峰、偏态、多峰三种类型；还涵盖指数随机图模型与机理网络模型，二者均由难解似然定义，从中模拟大规模网络数据集的计算成本极高。本文还研究了ABC中模拟成本问题的一种新解决方案。通过对大规模真实网络的分析，研究进一步阐释了copulaABcdrf框架与标准ABC方法的效果。文章最后总结了模拟研究与实证研究的结果，以及这些结果对未来研究的启示。关键词：贝叶斯分析，最大似然，难解似然。
英文摘要：
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.
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