Abstract

For many decades now, Bayesian Model Averaging (BMA) has been a popular framework to systematically account for model uncertainty that arises in situations when multiple competing models are available to describe the same or similar physical process. The implementation of this framework, however, comes with a multitude of practical challenges including posterior approximation via Markov chain Monte Carlo and numerical integration. We present a Variational Bayesian Inference approach to BMA as a viable alternative to the standard solutions which avoids many of the aforementioned pitfalls. The proposed method is “black box” in the sense that it can be readily applied to many models with little to no model-specific derivation. We illustrate the utility of our variational approach on a suite of examples and discuss all the necessary implementation details. Fully documented Python code with all the examples is provided as well.

摘要

几十年来，贝叶斯模型平均 (BMA) 一直是一种流行的框架，用于系统地解释在多个竞争模型可用于描述相同或相似的物理过程的情况下出现的模型不确定性。然而，该框架的实施伴随着许多实际挑战，包括通过马尔可夫链蒙特卡洛的后验近似和数值积分。我们提出了 BMA 的变分贝叶斯推理方法作为标准解决方案的可行替代方案，避免了许多上述缺陷。所提出的方法是“黑匣子”，因为它可以很容易地应用于许多模型，几乎不需要模型特定的推导。我们在一组示例中说明了变分方法的实用性，并讨论了所有必要的实现细节。还提供了包含所有示例的完整记录的 Python 代码。