MMM - Working with prior knowledge

[cetagostini]

Hey guys!

I was playing with adding prior knowledge to the model, but sadly I'm not seeing the expected results. So, I wanna ask the following.

1. How the prior is modeling the behavior of the model?
2. Which parameter should be changing once we add channel_prior?

Why am I asking?

Currently, I was adding prior knowledge to previous pymc models defining the values that were required for each type of distribution.

Example: I have prior knowledge about a specific channel, basically, I know the mean contribution to the target variable should be around 0.02. Using heuristic estimation, I could define how wide would be the distribution (based on how much I believe in the prior knowledge) and using the data define alpha/beta values to the distribution.

# Mean and shaping constant
mean_channel = 0.02
c = 85  # Shaping constant

# Calculate alpha and beta for Beta distribution
prior_alpha = mean_channel * c
prior_beta = (1 - mean_channel) * c

print("Alpha:", prior_alpha)
print("Beta:", prior_beta)

Here is an example where I create a couple of distributions, where the Google iOs is centered around the 0.02 value with strong beliefs, the other distribution as weaker beliefs. Finally, this is then added to the model as a list of alphas and betas to the DelayedSaturatedMMM. Here is my implementation ->

mmm = DelayedSaturatedMMM(
    data = df,
    target_column="y",
    date_column="ds",
    channel_columns = channels,
    control_columns=[
        'monthly', 
        'quarterly', 
        'yearly', 
        'trend'
    ],
    adstock_max_lag=2,
    channel_prior = pm.Beta.dist(alpha=prior_alpha, beta=prior_beta),
)

The problem

I'm doing this iterating with several values of alphas and betas but the results are the same. Looks like the model is ignoring the signal of the prior distribution and is only trying to fit as usual. So, not sure what I'm doing wrong in this implementation. Which makes me ask the first two questions 😅