This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a measure of uncertainty is necessary when change point methods are deployed in sensitive applications, for example, when one is interested in determining whether an organ is viable for transplant. The key of our proposal is framing the problem as a product of multiple single changes in the scale parameter. We fit the model through an iterative procedure similar to what is done for additive models. The novelty is that each iteration returns a probability distribution on time instances, which captures the uncertainty in the change point location. Leveraging a recent result in the literature, we can show that our proposal is a variational approximation of the exact model posterior distribution. We study the algorithm's convergence and the change point localization rate. Extensive experiments in simulation studies illustrate the performance of our method and the possibility of generalizing it to more complex data-generating mechanisms. We apply the new model to an experiment involving a novel technique to assess the viability of a liver and oceanographic data.

翻译：本文提出了一种新颖的贝叶斯方法，用于检测高斯序列模型中的方差变化，重点在于量化变点位置的不确定性，并提供了一种可扩展的推理算法。当变点方法应用于敏感场景（例如，判断器官是否适合移植）时，这种不确定性度量是必要的。我们方法的关键在于将问题建模为尺度参数中多个单一变化的乘积。通过类似于加性模型的迭代过程来拟合模型。其新颖之处在于，每次迭代都会返回一个时间点上的概率分布，该分布捕捉了变点位置的不确定性。利用文献中的最新成果，我们可以证明我们的提议是对精确模型后验分布的变分近似。我们研究了算法的收敛性以及变点定位速率。大量模拟实验展示了我们方法的性能，以及将其推广到更复杂数据生成机制的可能性。我们将新模型应用于一项涉及评估肝脏存活能力的新技术实验以及海洋学数据。