Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a large simulated dataset. This provides a generator that we can evaluate at the observed data and provide draws from the posterior distribution. This method applies to all forms of Bayesian inference including parametric models, likelihood-free models, prediction and maximum expected utility problems. Bayesian computation is then equivalent to high dimensional non-parametric regression. Bayes Gen-AI main advantage is that it is density-free and therefore provides an alternative to Markov Chain Monte Carlo. It has a number of advantages over vanilla generative adversarial networks (GAN) and approximate Bayesian computation (ABC) methods due to the fact that the generator is simpler to learn than a GAN architecture and is more flexible than kernel smoothing implicit in ABC methods. Design of the Network Architecture requires careful selection of features (a.k.a. dimension reduction) and nonlinear architecture for inference. As a generic architecture, we propose a deep quantile neural network and a uniform base distribution at which to evaluate the generator. To illustrate our methodology, we provide two real data examples, the first in traffic flow prediction and the second in building a surrogate for satellite drag data-set. Finally, we conclude with directions for future research.

翻译：开发了贝叶斯生成式AI方法并将其应用于贝叶斯计算。直接通过将感兴趣的参数建模为大规模模拟数据集上的映射（即深度学习器），贝叶斯生成式AI重构后验分布。该方法提供一个在观测数据上可评估的生成器，从而生成来自后验分布的样本。本方法适用于所有形式的贝叶斯推断，包括参数模型、无似然模型、预测及最大期望效用问题。此时，贝叶斯计算等价于高维非参数回归。贝叶斯生成式AI的主要优势在于其无需密度函数，因此为马尔可夫链蒙特卡洛提供了替代方案。相比传统生成对抗网络和近似贝叶斯计算方法，该方法具有若干优势，原因在于其生成器相较于GAN架构更易学习，且比ABC方法中隐含的核平滑更具灵活性。网络架构设计需要谨慎选择特征（即降维）并配置用于推断的非线性架构。作为通用架构，我们提出深度分位数神经网络及均匀基分布用于评估生成器。为展示方法论，我们提供两个真实数据案例：其一为交通流预测；其二为卫星阻力数据集代理模型构建。最后，我们给出未来研究方向。