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 prior type can be specified for each treatment type. The ModelSpec contains arguments media_prior_type, rf_prior_type, organic_media_prior_type, organic_rf_prior_type, and non_media_treatments_prior_type, which allow you to specify whether a prior is placed on ROI, mROI, contribution, or the coefficient mean. (ROI and mROI priors are only available for paid media.)

The PriorDistribution object has an argument for each combination of treatment type and prior type. For each treatment type, only the argument corresponding to the selected prior type is used. The others are ignored. For example, the arguments corresponding to non-R&F paid media are roi_m, mroi_m, contribution_m, and beta_m. If media_prior_type is 'roi', then roi_m is used and the others are ignored.

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

Paid media

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 media_prior_type and rf_prior_type arguments in ModelSpec. The model parameterization and default priors also depend on whether outcome is revenue. Outcome is revenue when either the KPI is revenue or when revenue_per_kpi is passed to InputData. Outcome is not 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
media_prior_type/rf_prior_type	Outcome	Prior Type	Parameter in PriorDistribution
'roi' (default)	Revenue	ROI	roi_m, roi_rf
'roi' (default)	Non-revenue	Total paid media contribution	roi_m, roi_rf
'mroi'	Revenue	mROI	mroi_m, mroi_rf
'mroi'	Non-revenue	No default, must set custom	mroi_m, mroi_rf
'contribution'	Revenue	Contribution	contribution_m, contribution_rf
'contribution'	Non-revenue	Contribution	contribution_m, contribution_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, mROI, and Contribution see ROI, mROI, and Contribution parameterizations. 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

The default prior for treatment effects of organic media is specified by the organic_media_prior_type and organic_rf_prior_type arguments. The options are 'contribution' and 'coefficient', with 'contribution' being the default. If contribution priors are used, then a prior distribution is specified on the contribution_om and contribution_orf parameters. If coefficient priors are used, then a prior distribution is specified on the beta_om and beta_orf parameters.

Non-media treatments

The default prior for treatment effects of non-media_treatments is specified by the non_media_treatments_prior_type argument. The options are 'contribution' and 'coefficient', with 'contribution' being the default regardless of whether the outcome is revenue. If contribution priors are used, then a prior distribution is specified on the contribution_n parameter. If coefficient priors are used, then a prior distribution is specified on the gamma_n parameter.