  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.
