Generative AI (Gen-AI) methods are developed for Bayesian Computation. Gen-AI naturally applies to Bayesian models which can be easily simulated. First, we generate a large training dataset of data and parameters from the joint probability model. Secondly, we find a summary/sufficient statistic for dimensionality reduction. Thirdly, we use a deep neural network to uncover the inverse Bayes map between parameters and data. This finds the inverse posterior cumulative distribution function. Bayesian computation then is equivalent to high dimensional regression with dimensionality reduction (a.k.a feature selection) and nonlnearity (a.k.a. deep learning). The main advantage of Gen-AI is the ability to be density-free and hence avoids MCMC simulation of the posterior. Architecture design is important and we propose deep quantile NNs as a general framework for inference and decision making. To illustrate our methodology, we provide three examples: a stylized synthetic example, a traffic flow prediction problem and a satellite data-set. Finally, we conclude with directions for future research.

翻译：本文开发了基于生成式人工智能（Gen-AI）的贝叶斯计算方法。Gen-AI自然适用于可便捷模拟的贝叶斯模型。首先，我们从联合概率模型中生成了包含数据和参数的大规模训练数据集；其次，通过降维技术提取汇总/充分统计量；然后，利用深度神经网络揭示参数与数据之间的逆贝叶斯映射，从而得到逆后验累积分布函数。此时，贝叶斯计算等价于结合降维（即特征选择）与非线性（即深度学习）的高维回归。Gen-AI的核心优势在于无需密度估计，从而避免了后验的MCMC模拟。网络架构设计至关重要，我们提出深度分位数神经网络作为推理与决策的通用框架。为验证方法有效性，本文给出了三个案例：标准合成示例、交通流预测问题及卫星数据集。最后，我们展望了未来研究方向。