Probabilistic Estimation

Probabilistic Estimation

This section provides tools and reference data for quantifying delegation risk using probability distributions rather than point estimates.

Why Probabilistic?

Most risk frameworks use point estimates like “probability = 2%” or “damage = $5,000”. This approach:

• Understates uncertainty in our knowledge
• Hides tail risk from rare-but-severe events
• Prevents sensitivity analysis to identify critical parameters
• Blocks Bayesian updating as we gather more data

By expressing estimates as probability distributions, we can propagate uncertainty through calculations and make better-informed decisions.

What’s Included

Interactive Tools

Calculators and visualizations for applying probabilistic methods:

• Risk Calculator: Monte Carlo simulation with budget confidence analysis
• Trust Updater: Bayesian belief updating based on track record
• Sensitivity Dashboard: Identify which parameters drive your risk
• Architecture Comparator: Compare delegation architectures side-by-side

Estimates Registry

Calibrated probability distributions for key risk parameters:

• Probability Priors: Failure rates by component type
• Damage Distributions: Cost magnitudes by category
• Mitigation Effectiveness: Risk reduction from various interventions
• Trust Calibration: Bayesian updating formulas
• Cross-Domain Benchmarks: Reference points from nuclear, aviation, finance
• Expert Elicitation Guide: How to gather calibrated estimates
• Incident Database Integration: Grounding estimates in real data

Getting Started

1. Explore the estimates to understand the baseline distributions
2. Use the Risk Calculator to model your specific situation
3. Apply the Trust Updater as you gather operational data
4. Run sensitivity analysis to focus mitigation efforts

Technical Foundation

We use Squiggle notation for distributions:

• beta(a, b) for probabilities (bounded 0-1)
• lognormal(mu, sigma) for damages (heavy-tailed, positive)
• mixture([d1, d2], [w1, w2]) for multi-modal outcomes

The interactive tools use Monte Carlo simulation (10,000 samples) to propagate uncertainty.