Safe R
Safe D
Seat Distribution
Competitive Races
Hierarchical Bayesian election forecasting model for the 2026 U.S. Senate (35 races), estimated via Stan HMC (Hamiltonian Monte Carlo). Constructs a fundamentals-based prior per race from recency-weighted presidential lean, generic congressional ballot (GCB), presidential approval, incumbency advantage, and candidate quality. Key structural parameters—incumbency bonus, GCB-to-Senate coefficient, presidential lean weight, and poll bias—are jointly estimated in Stan with bounded informative priors centered on values from the political science literature, propagating structural uncertainty into the forecast rather than conditioning on fixed point estimates. Polls are incorporated via a hierarchical Stan model with Student-t poll likelihood (robust to outliers), national and regional random effects, and jointly estimated poll bias and degrees of freedom. Partial pooling across states within 4 regions borrows strength from related races. States with unresolved primaries are modeled as probability-weighted nominee scenarios with an additional uncertainty bonus reflecting the unknown matchup.
Uncertainty is propagated through 50,000 Monte Carlo draws from the Stan posterior, plus three forward-looking drift layers: national GCB drift (fat-tailed t-distribution), regional correlated drift, and state-level idiosyncratic drift. Drift magnitudes are time-dependent, scaling by √(months to election / 8). The model is validated against 8 historical cycles (2010–2024) via leave-one-cycle-out cross-validation; the backtest is used for calibration diagnostics, not parameter optimization, since the loss surface is flat over wide parameter ranges with only 8 cycles.
Prediction intervals are constructed using conformal inference on backtest residuals (actual margin minus posterior mean across all 8 historical cycles). Ten variants are compared, including split conformal, stratified Mondrian, locally-adaptive, recency-weighted, conformalized quantile regression (CQR), Jackknife+, and Conformal Bayes variants. Coverage is validated via leave-one-cycle-out (honest 90% coverage: 89.9%), yielding finite-sample coverage guarantees without distributional assumptions.
The National Environment slider adjusts the generic congressional ballot (GCB)—a measure of the national partisan mood derived from polls asking voters which party they prefer for Congress—with presidential approval tied via a recalibrated midterm approval-GCB relationship. The Customize Assumptions panel lets you override three structural parameters: incumbency advantage (how much sitting senators benefit from holding office), national mood effect (how strongly the GCB translates to individual Senate race margins), and polling bias (systematic overestimate of Democratic margin in polls). Adjustments shift race margins additively, with win probabilities and seat totals recomputed in real time.