Not all MMMs are created equal. At Recast, we’ve embraced a Bayesian approach to MMM because it allows for more flexibility and actionable insights than traditional methods.
However, the success of any Bayesian MMM hinges on one critical element: good priors.
This article explores why priors are so important, how we at Recast set them, and the steps we take to make sure they lead to accurate, reliable, and actionable results.
1. What Are Priors in a Bayesian Model?
In Bayesian statistics, priors represent what we know (or believe) about the world before we start analyzing data. They act as a starting point for the model and influence the results, particularly when data is sparse or noisy.
For example:
- Positive ROI: It’s unlikely that spending money on advertising will reduce sales, so a prior might suggest that the ROI of a channel should be positive.
- Base Demand: A well-known brand likely has a high base level of sales that occurs without paid marketing, while a newer brand relies more on advertising to generate revenue.
Without priors, a statistical model may produce nonsensical results. Without priors to constrain ROI estimates, we’ve seen models say that spending on Facebook ads decreases sales – an outcome that just doesn’t make sense.
I know that seems basic, but, if you were to build a statistical model on a marketing dataset without priors, you would almost certainly get negative ROIs back.
In simple terms, priors translate what marketers already know into mathematical language, which constrains the model so that it reflects reality. But getting them right isn’t easy.
2. How Recast Sets Priors
At Recast, we’ve developed a rigorous process for setting priors that ensures our Bayesian MMMs are both accurate and aligned with business realities. Here’s how we do it:
Step 1: Base Demand Estimation
The first step is to estimate the base level of demand, which is the portion of sales that occurs organically, independent of paid marketing.
- Established Brands: Older brands with strong recognition may have 70–80% of their sales come from organic sources like word of mouth or repeat purchases.
- Challenger Brands: Newer brands often rely heavily on paid marketing, with only 20–30% of sales coming from organic channels.
The goal here is to contextualize the impact of paid advertising. For example, if a brand generates $10 million in revenue annually and 70% is organic, paid marketing should account for the remaining $3 million.
Step 2: ROI and CPA Priors
Once we know the base demand, we set priors for ROI and CPA. These priors keep the model’s estimates for channel performance reasonable and consistent with the overall business data.
Calculating ROI Priors: We use a straightforward formula:

For example, if a brand generates $10 million in total revenue, with $6 million from organic sources and $2 million in ad spend, the average ROI for paid marketing would be 2x.
We also account for channel-level variation. For instance:
- Paid search might deliver a 5x ROI.
- Display ads might hover around 1.5x.
Step 3: Timeshift Priors
Advertising effects don’t always happen immediately. Timeshift priors account for how long it takes for ad spend to translate into measurable results.
- Impulse Purchases: ads for low-cost items might drive immediate sales.
- High-Consideration Purchases: for products like cars or furniture, the effects of advertising might take weeks to materialize.
Each channel has its own “shift curve.” For example:
- TV Ads: these might drive awareness that translates into sales weeks later.
- Direct Mail: effects might peak days or weeks after delivery, as recipients take time to respond.
Step 4: Prior Predictive Checks
Before fitting the model to actual data, we validate the priors through simulations. This involves running the model using only the priors to make sure they produce plausible results.
What we’re looking for here is to see if the simulated outcomes are within the ballpark of real-world expectations and if they align with the brand’s historical performance.
If the simulations suggest implausible results—like predicting 10x more sales than the brand has ever achieved—we have to go back and adjust the priors.
Step 5: Parameter Recovery Checks
Finally, we need to see if the model can accurately infer the parameters that generated simulated data, and we do this through parameter recovery checks.
First, we simulate data using known parameters (e.g., ROI, timeshifts, base demand), and then we run the model to see if it can recover these parameters. If the model struggles to identify the correct parameters, we refine the priors and repeat the process.
This helps us create models that are both data-driven and aligned with marketing intuition. It’s a delicate balance, but one that’s crucial for accurate, actionable insights.
T..L; D.R:
- Priors translate what marketers already know about their business into a form the model can use. A model is only as good as its assumptions.
- The Recast process for priors:
- Start with base demand
- Set ROI/CPA priors
- Timeshift priors
- Prior predictive checks
- Parameter recovery checks