Media Mix Modeling (MMM) is a methodology for distributing marketing spend efficiently across acquisition channels for the purposes of optimizing some business outcome (clicks, installs, revenue, etc.). With Media Mix Modeling, an analyst, CMO, or some other marketing executive is trying to optimize the overall impact of the marketing budget across a portfolio of marketing channels via budget distribution. MMM takes a macro view of the marketing budget versus attribution optimization, which takes a micro view at the level of the individual channel (or even at the level of a campaign within a channel).
There are a few different popular approaches to implementing MMM into a marketing organization. One is to build a fairly simple regression model that seeks to estimate the impact of spend on each channel by isolating channel spend (budget) and marginal channel contribution (installs, conversions, revenue, etc.) and then finding an optimal mix of channel-budgets. A good overview of such an approach can be found in this article by a former Uber marketer. The problem with this approach is that channel budgets are often highly correlated: the overall marketing budget fluctuates based on a number of factors that may have very little to do with the performance of a given marketing channel or even the performance of the total channel portfolio, and so the data when these periods of "scale-up" and "pull back" exhibit a high level of covariance and the model requires a regularization variable to avoid overfitting.
Another popular approach (and the one I prefer) is a Bayesian Bandits system that avoids the need for regularization by using Bayesian priors for the distribution of each channel and adjusting them over some regular interval via the explore / exploit process. This dissertation from a master's student at Aalto University in Finland provides a very thorough and deft framework for thinking through such a solution, as applied to Facebook advertising. It should be noted that Facebook's new Campaign Budget Optimizer product already does this across Facebook campaigns.