Eight channels, one budget,
and an honest answer.

104 weeks of weekly observations for a fictional mid-market beauty brand selling on its own DTC site, Walmart, and Sephora. Eight marketing channels, weekly revenue, and four control variables (seasonality, holidays, competitor pressure, price promotions). All numbers are generated from documented ground-truth coefficients and a fixed seed, so the entire simulation is reproducible.

-- Pull 104 weeks of channel spend + revenue for the modeling dataset.
-- Weekly grain. Sunday-anchored ISO weeks. All channels left-joined so
-- weeks with zero spend on a channel still appear (zero-spend weeks
-- are signal, not noise).
SELECT
  d.iso_week,
  d.year_week,
  rev.gross_revenue,
  rev.units_sold,
  SUM(IF(s.channel = 'tiktok_creator',    s.spend, 0)) AS tiktok_creator_spend,
  SUM(IF(s.channel = 'instagram_creator', s.spend, 0)) AS instagram_creator_spend,
  SUM(IF(s.channel = 'youtube_creator',   s.spend, 0)) AS youtube_creator_spend,
  SUM(IF(s.channel = 'meta_paid',         s.spend, 0)) AS meta_paid_spend,
  SUM(IF(s.channel = 'tiktok_paid',       s.spend, 0)) AS tiktok_paid_spend,
  SUM(IF(s.channel = 'paid_search',       s.spend, 0)) AS paid_search_spend,
  SUM(IF(s.channel = 'programmatic',      s.spend, 0)) AS programmatic_spend,
  SUM(IF(s.channel = 'retail_media',      s.spend, 0)) AS retail_media_spend,
  ctrl.competitor_idx,
  ctrl.price_discount_active,
  ctrl.holiday_label
FROM      `imm_lab.dim_week`              d
LEFT JOIN `imm_lab.fct_revenue_weekly`    rev   USING (iso_week)
LEFT JOIN `imm_lab.fct_channel_spend_wk`  s     USING (iso_week)
LEFT JOIN `imm_lab.dim_controls`          ctrl  USING (iso_week)
WHERE     d.iso_week BETWEEN '2024-01-01' AND '2025-12-28'
GROUP BY  d.iso_week, d.year_week, rev.gross_revenue, rev.units_sold,
          ctrl.competitor_idx, ctrl.price_discount_active, ctrl.holiday_label
ORDER BY  d.iso_week;

Marketing Mix Models decompose weekly revenue into channel contributions, baseline demand, and external factors. The two transformations that make the math work for marketing data are adstock (carryover effects: a creator post on Tuesday still drives sales on Friday) and saturation (each additional dollar buys less response than the dollar before it). A Bayesian fit gives credible intervals on every coefficient, which is what budget decisions actually need.

Each channel's share of total revenue across the 2-year panel, with 90% credible intervals. Total ROAS tells you the average dollar back per dollar in. Marginal ROAS (mROAS) tells you the next dollar back per next dollar in — which is what budget reallocation actually depends on.

For each channel, the spend → response curve with 90% credible bands. The vertical line marks current weekly spend. Channels where the line sits deep on the plateau are saturated — the next dollar buys very little. Channels where the line is still on the steep part are still in linear territory and reward more spend.

Move budget between channels. The model recomputes weekly revenue under the new mix using each posterior sample, returning a 90% credible interval on the predicted lift versus the current allocation. Hold the total budget constant or let it flex.

Because the data is synthetic, the channel coefficients used to generate it are known. At a nominal 90% credible interval, expected coverage on 8 channels is 7.2 — over-coverage at exactly 8/8 would suggest the priors are too wide or the CIs over-inflated. Below, each row shows the ground-truth α (max contribution), the posterior mean, and the 90% credible interval. The recovery count is rendered live from the model.json that ships with the page; if you re-run the notebook the count below updates automatically.