Anomaly Detection with Gaussian Processses (from GP tutorial)

I’ve just seen the Intro to gaussian process video on the Stan youtube channel, which is great. It talks about fitting GPs to astronomical data in order to detect exoplanets, as explained here in the video. Basically, when planet passes in front of a star there is a brief dip in the light intensity. The tutorial explains how to fit the GP model, which captures general trends, but doesn’t say how to detect these dips in signal using the fitted posterior. How would one go about this?

For background, I’m working on a similar problem in bioinformatics, using a latent GP to model spatial variation in count data. I’ve adapted the model in Michael Betancourt’s excellent Robust GPs with Stan tutorial, which is working well, I think (I’m getting a good visual fit to the background data), but now I want to detect local dips in signal, relative to the fitted background, in a principled way.