Default prior parameterizations

Meridian offers multiple ways to parameterize the causal effect of each treatment variable on the KPI. We refer to each option as different model parameterizations. In Bayesian inference, a prior must be set on the parameters of the model. So the model parameterization determines what precisely one is setting a prior on.

The paid_media_prior_type argument of the ModelSpec lets you specify whether a prior is placed on ROI, mROI, or the coefficient (beta_m). The PriorDistribution object has arguments for roi_m, mroi_m and beta_m, but only one will be used depending on the value of paid_media_prior_type. Likewise, the PriorDistribution object has arguments for roi_rf, mroi_rf, and beta_rf, but only one will be used depending on the value of paid_media_prior_type.

Each model parameterization has a different default prior distribution. The following tables summarize the default priors under each model parameterization.

The following table summarizes the model parameterization and default priors for the causal effect of paid media on the KPI. These vary based on the paid_media_prior_type argument in ModelSpec. The model parameterization and default priors also depend on whether outcome is in terms of revenue. Outcome is in terms of revenue when either the KPI is revenue or when revenue_per_kpi is passed to InputData. Outcome is not in terms of revenue ("non-revenue") when the KPI is not revenue and revenue_per_kpi is not passed to InputData. The table also includes a column indicating the corresponding parameter in the PriorDistribution container that allows one to customize the prior.

Model Type Default Prior
paid_media_prior_type Outcome Prior Type Parameter in PriorDistribution
'roi' (default) Revenue ROI roi_m, roi_rf
'roi' (default) Non-revenue Total Paid Media roi_m, roi_rf
'mroi' Revenue mROI mroi_m, mroi_rf
'mroi' Non-revenue No default, must set custom mroi_m, mroi_rf
'coefficient' Revenue Coefficient beta_m, beta_rf
'coefficient' Non-revenue Coefficient beta_m, beta_rf

The distribution used as the default prior for each model parameterization is summarized in Default prior distributions.

Under each scenario listed in the table, set a custom prior using the appropriate PriorDistribution parameter indicated in the table. When setting a custom prior, it's important to understand what you are setting a custom prior on. For more on the definition of ROI and mROI, see ROI and mROI parameterization. For more on the definition of a coefficient, see the model specification. For more on the total paid media contribution prior, see Custom total paid media contribution prior.

Organic media and non-media treatments

The default prior for treatment effects of organic media and for non-media treatments are unaffected by the paid_media_prior_type argument nor are they affected by whether or not the KPI is revenue. Organic media uses beta_om or beta_orf as its prior parameter and non-media treatments uses gamma_n as its prior parameter.