Bernoulli CUSUM and Bayes-Optimal Detection Ceilings for Trust Fraud in Sparse Rating Networks

Abstract: Sequential trust detection in rating networks relies on continuous observation models that fail on real data. On Bitcoin-OTC, 56\% of ratings take a single value under standard mapping, breaking the distributional assumptions that parametric detectors require. This paper makes three contributions. It derives a Bayes-optimal F1 detection ceiling for per-node sequential detectors using empirically measured observation parameters. At Bitcoin-OTC's median in-degree of 2, this ceiling falls to 0.451 for strategic attacks, explaining why unsupervised methods cluster near $F1 \approx 0.4$. The analysis shows that detector-model matching, not information content, determines performance: binary models retain 86\% of mutual information while enabling exact parametric fit. A dual-regime architecture is presented where Bernoulli CUSUM detects behavioral shifts and triggers asymmetric scoring. Ablation reveals a co-design constraint: the modulation mechanism improves AUC by 0.030 on binary observations but degrades it by 0.094 on continuous observations. The combined system achieves AUC 0.749 on Bitcoin-OTC and 0.796 on Bitcoin-Alpha, beating GaaSTrust on all 8 attacks ($p < 0.003$), with founder-label AUC of 0.999.