Posterior Mean
39.8%
Expected Viability Share
Posterior SD
0.024
Uncertainty Standard Dev
Win Probability
88.4%
Chance Candidate Gains Viability
Median EVs
284
Electoral Votes (50th Pct)
P-Value vs Null
0.012
Null: Viability < 30%
1. Bayesian Updating Distribution Curves (Prior vs Likelihood vs Posterior)
Prior
Poll Likelihood
Posterior
2. Monte Carlo Electoral College Simulation (5,000 Iterations)
< 270 EVs (Loss)
≥ 270 EVs (Win)
Political Presets
Interactive Parameter Scrubbers
Historical Prior Mean (μ0)
35.0%
Candidate initial baseline viability standard.
Prior Standard Dev (σ0)
8.0%
Uncertainty surrounding historical candidate baseline.
Fresh Poll Support Mean (μx)
42.0%
Observed support share in latest polling aggregation.
Poll Sample Size (N)
1,000
Directly determines polling variance & margin of error.
Battleground State Correlation (ρ)
0.65
Systemic polling error shared across swing states.
Monte Carlo Simulations
5,000
95% Credible Interval & Margin of Error
Poll Margin of Error:
±3.1%
95% Posterior Interval:
[35.1%, 44.5%]
Prior vs Poll Weight:
3.7% / 96.3%
Canonical Statistical State & Bayesian Updating Derivation
Conjugate Normal Formulas
1/σ²post = 1/σ²prior + 1/σ²poll
μpost = σ²post (μprior/σ²prior + μpoll/σ²poll)
μpost = σ²post (μprior/σ²prior + μpoll/σ²poll)
Representative Fixture Verification
Prior: N(0.35, 0.08²)
Poll: N(0.42, 0.0156²) with N=1,000
Computed Posterior Mean: 0.398
Poll: N(0.42, 0.0156²) with N=1,000
Computed Posterior Mean: 0.398
Monte Carlo Electoral Model
Base Safe EVs: 210
Battleground EVs: 93 (PA, MI, WI, GA, NC, AZ, NV)
Win Odds (≥270 EVs): 88.4%
Battleground EVs: 93 (PA, MI, WI, GA, NC, AZ, NV)
Win Odds (≥270 EVs): 88.4%