For each scenario s and setup m, p[s, m] ~ Beta(a, b) and each completed outcome Y[i, s, m] | p ~ Bernoulli(p), so k | p ~ Binomial(n, p). Y = 1 when a simulated payment executes with positive unauthorized exposure. Errors do not enter n.
The posterior Beta(a + k, b + n − k) is a deterministic calculation from the prior and the observed counts. Its mean is (a + k) / (a + b + n); intervals are 95% equal-tailed Bayesian credible intervals. A cell with n = 0 is prior only and has no empirical rate.
The weighted projection Σ w[s] p[s, m] uses independent scenario priors and reproducible posterior draws. The weights are an illustrative assumed traffic mix that must sum to one.
The exact upper endpoint is a fixed-sample, one-sided Clopper–Pearson bound with α = 0.05/24 per cell, giving simultaneous 95% coverage across 24 cells under i.i.d. outcomes within each cell. The weighted endpoint Σ w U is shown only when every predetermined held-out outcome is complete and resolved. It is not an anytime bound.
The four setups replay the same saved proposals on fresh identical ledgers. Outcomes are paired, not independent, so no probability that one setup is superior is reported. The probability graph is separate from the agent topology and does not imply independence between workflow components.
Model checks report prior sensitivity, exact posterior variance under independent scenario priors, and conservative paired probability-difference bounds derived from discordant case pairs. The paired bounds have a separate 5% family error budget; together with the original frequency bounds, these are not a joint 95% guarantee. Known-truth simulation results and derivations are documented in the statistical audit.
Synthetic orders and money. Estimates describe the selected test workload.