Priors as Controls

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?

I am not sure about how to use priors that context. Usually when I am thinking of time series data I look to state space models (there are many other choices too!) In which there is an event that alters the system that we code up like an intervention (0, 1’s after the event). But there are other events happening so I include those as covariates with the priors attached to them.

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