Deciding the right marketing channels and how to measure effect is the eternal problem for all marketers. For digital channels one has partly solved this with attribution (follow your customers from view/click to sales), but privacy concerns are eroding that capability.
With marketing mix models, one instead focus of what you have done of marketing activities historically and how sales react after. This type of sales modeling has a long history, but are in a riveting development which gives much more stable and usable models and what one had before.
There are several advantages of the bayesian approach, but a lot comes down to two points:
In traditional sales modeling, one create the models based upon data directly. The problem with this is that you usually have quite few datapoints and many parameters one wants to find. This lead to several models that might be as statistical sound as each other, and it is up to the analyst to chose which. But if they do not resonate with the prior knowledge of the business, it is possible to chose another model which is as statistical sound but gives totally different results.
With the bayesian approach that are made possible with modern machine power and algortihms, one instead explisity interview the business for what they make their allocations for today and make a model based on this. In theory we could stop here, and optimize the budget after how you think the different channels behave.
However, what we do is that we take your expert knowledge as a starting point, and then we update the models week for week and adjust it towards what the data tell us. This combination makes for stronger and more stable models.
Another advantage is that everything is a distribution in this setting, and we know and can be explisit about how unsure we are of the different parameters in the model. So if you spend a lot on a channel, but we can not be certain about the results, we can help to design an experiment which we again can use in the model and make it stronger.
Important that this is to optimize between the different channels, to optimize how to actually run Google, attribution and tracking is still very Important tools.