Instantiating Priors for Contribution Media Type

[paul-jdfagan]

Hello Meridian Devs,

I'm having trouble instantiating priors for contribution media type. In my case, I have a couple of experiments I want to include in the model and leave the remaining channels to the default prior. I see lots of excellent documentation for ROI prior type but less for the Contribution prior use case. Any help would be much appreciated.

I know I need to translate a mean and SE to a beta distribution per the docs.

import numpy as np
import tensorflow_probability.substrates.numpy.distributions as tfd
from meridian.model import prior_distribution, spec, model
import meridian.constants as constants

#  Lift test results
calibrated = {
    "channel1": {"mean": 0.12, "se": 0.03},
    "channel2": {"mean": 0.15, "se": 0.025},
}

#  Estimate Beta parameters
def estimate_beta_params(mean, se):
    var = se**2
    sum_params = (mean * (1 - mean)) / var - 1
    return mean * sum_params, (1 - mean) * sum_params

#  Build prior lists in order of paid channels
alpha, beta = [], []
for ch in data.get_all_paid_channels():
    if ch in calibrated:
        a, b = estimate_beta_params(calibrated[ch]["mean"], calibrated[ch]["se"])
    else:
        a, b = 2.0, 8.0  # Regularizing default
    alpha.append(a)
    beta.append(b)

#  Build batched Beta prior
contribution_prior = tfd.Beta(
    concentration1=np.array(alpha, dtype=np.float32),
    concentration0=np.array(beta, dtype=np.float32),
    name=constants.CONTRIBUTION_M
)

#  Plug into model
prior = prior_distribution.PriorDistribution(contribution_m=contribution_prior)

model_spec = spec.ModelSpec(
    prior=prior,
    media_effects_dist="log_normal",
    media_prior_type="contribution",
    holdout_id=holdout_id,
    knots=20
)

mmm = model.Meridian(input_data=data, model_spec=model_spec)

[cpulavarthi]

Hello @paul-jdfagan,

Thank you for contacting us!

Your code for initializing contribution priors appears correct to me and is also executing without errors. The default beta distribution parameters used in Meridian are (1, 99) but you are using (2, 8) as the default values of alpha and beta in your code, I am assuming that this is intentional and makes business sense for your use case. The function estimate_beta_params(mean, se) is also defined correctly and returns alpha and beta parameters for the corresponding Beta distribution. Can you share the details of any specific issues you may be facing while attempting to instantiate contribution priors?

You may check our API documentation on Prior Distributions for a detailed list of model parameters that accept prior distributions, and what they default to in the absence of setting them specifically.

Do reach out with additional information regarding the specific issues you are facing so that we can help you better.

Google Meridian Support Team