Weather is multi-dimensional. Rules collapse it to one variable. The model sees everything.
The demand curve is not what you think.
Sunscreen demand drops above 105°F — people stay indoors. Hot coffee has two regimes. HVAC has distinct activation thresholds. Toggle between categories and watch the non-linear response surface morph in real time.
Simple rules assume linear relationships. The real demand surface has thresholds, saturation points, and inversion zones. A model trained on multi-variable weather data captures what intuition cannot.
Day one feels like year two.
Traditional tools treat each brand in isolation. Thagorus uses partial pooling — a mathematically proven technique from the James-Stein theorem (1961) — to borrow strength across similar brands. Drag the slider and watch prediction error collapse as the network grows.
Live patterns across 47 markets. When one market hits a threshold, every similar market gets a tighter estimate.
“When estimating 3 or more means simultaneously, the individual estimate is inadmissible.”James & Stein (1961)
Every recommendation comes with its own proof.
Every recommendation ships with an evidence bundle. Not a black box confidence score — a complete forensic breakdown. Here’s one from last weekend.
Every category gets its own evidence bundle. The model adapts to each product’s unique weather-demand signature.
The Race: Model vs. Rules over 52 Weeks
Watch as the model (green) consistently tracks actual demand while rule-based approaches (red) accumulate error.
Synthetic backtests with known ground truth.
Before any model touches a dollar of ad spend, we generate synthetic demand data with known weather elasticities—a known data-generating process (DGP)—fit the model, and verify parameter recovery. These are pre-launch benchmarks demonstrating methodological rigor, not production performance claims. The live show starts with our design partners in Q2 2026.
Methodology: Synthetic data with known DGP. Time-series cross-validation (expanding window, no lookahead bias). Hyperparameters selected via Bayesian search (Optuna) with MAPE as the selection criterion. Held-out results use markets never seen during training.
Caveat: These results are from synthetic data where the data-generating process matches the model’s assumptions. Real-world performance will differ due to model misspecification, unobserved confounders, and non-stationarity. We are committed to publishing production validation results as they become available from our design partner engagements.
Do 90% intervals contain the truth ~90% of the time?
Confidence without calibration is self-esteem. Thagorus uses adaptive conformal inference (Gibbs & Candès, 2021) extended to non-exchangeable data (Barber et al., 2023) to produce prediction intervals with guaranteed finite-sample coverage—even under distribution shift.
“Do confidence scores correlate with realized lift rather than with model self-esteem?”Thagorus Proof Obligation #2: Calibration
A system that cannot name its failures has not looked.
The strongest claim is a bounded claim. Thagorus ships every recommendation with explicit break conditions—the circumstances under which the recommendation should be reversed, widened, or withdrawn. Here is the full framework.
If you can audit these results—wins and losses—then we are not blowing smoke. We are doing science in public, which is rare enough to be a product feature.
Standing on the shoulders of giants.
Thagorus draws on a deep body of work across causal inference, econometrics, machine learning, and uncertainty quantification. Key citations organized by domain.