The derivation of key equations for the variational Bayes approach is well-known in certain circles. However, translating the fundamental derivations (e.g., as found in Beal's work) to Friston's notation is somewhat delicate. Further, the notion of using variational Bayes in the context of a system with a Markov blanket requires special attention. This Technical Report presents the derivation in detail. It further illustrates how the variational Bayes method provides a framework for a new computational engine, incorporating the 2-D cluster variation method (CVM), which provides a necessary free energy equation that can be minimized across both the external and representational systems' states, respectively.

翻译：变分贝叶斯方法关键方程的推导在特定学术圈内已广为人知。然而，将基础推导过程（例如Beal著作中的表述）转换至Friston的符号体系需格外审慎。此外，在具有马尔可夫毯的系统语境中应用变分贝叶斯的概念需要特别关注。本技术报告详细阐述了该推导过程，并进一步说明变分贝叶斯方法如何为新型计算引擎提供框架——该框架整合了二维团簇变分法（CVM），从而导出一个可在外部系统状态与表征系统状态上分别最小化的必要自由能方程。