I have a general question about Bayesian Regression Modeling and how a prior might be used as a means to control for (close to) simultaneous events. I often face a situation where I have a time series of sales and am looking to estimate the impact of an event (on the trend and level). This would be a candidate for an interrupted time series model - encoding periods post the event as 1 and 0 prior. The problem is that there are often other events that have not happened before, in close proximity time wise to the event of interest - maybe at the same time for all or part of the same time as the event of interest.
If I am willing to use ‘side information’ (maybe from subject matter experts or analysis in another region) …can I use a strong informative prior to ‘control’ for these other events and estimate the one I care most about?