Use when making predictions or judgments under uncertainty and need to explicitly update beliefs with new evidence. Invoke when forecasting outcomes, evaluating probabilities, testing hypotheses, calibrating confidence, assessing risks with uncertain data, or avoiding overconfidence bias. Use when user mentions priors, likelihoods, Bayes theorem, probability updates, forecasting, calibration, or belief revision.
Installer avec Codex ou Claude Copiez ce prompt, collez-le dans Codex, Claude ou un autre assistant, puis laissez-le vérifier la page du skill et l'installer pour vous.
Une commande directe contourne le prompt de vérification. Examinez la source avant de l'exécuter.
Use when making predictions or judgments under uncertainty and need to explicitly update beliefs with new evidence. Invoke when forecasting outcomes, evaluating probabilities, testing hypotheses, calibrating confidence, assessing risks with uncertain data, or avoiding overconfidence bias. Use when user mentions priors, likelihoods, Bayes theorem, probability updates, forecasting, calibration, or belief revision.
Apply Bayesian reasoning to systematically update probability estimates as new evidence arrives. This helps make better forecasts, avoid overconfidence, and explicitly show how beliefs should change with data.
When to Use This Skill
Making forecasts or predictions with uncertainty
Updating beliefs when new evidence emerges
Calibrating confidence in estimates
Testing hypotheses with imperfect data
Evaluating risks with incomplete information
Avoiding anchoring and overconfidence biases
Making decisions under uncertainty
Comparing multiple competing explanations
Assessing diagnostic test results
Forecasting project outcomes with new data
Trigger phrases: "What's the probability", "update my belief", "how confident", "forecast", "prior probability", "likelihood", "Bayes", "calibration", "base rate", "posterior probability"
What is Bayesian Reasoning?
A systematic way to update probability estimates using Bayes' Theorem:
P(H|E) = P(E|H) × P(H) / P(E)
Where:
P(H) = Prior: Probability of hypothesis before seeing evidence
P(E|H) = Likelihood: Probability of evidence if hypothesis is true
P(E|¬H) = Probability of evidence if hypothesis is false
P(H|E) = Posterior: Updated probability after seeing evidence
Quick Example:
# Should we launch Feature X?## Prior Belief
Before beta testing: 60% chance of adoption >20%
- Base rate: Similar features get 15-25% adoption
- Our feature seems stronger than average
- Prior: 60%
## New Evidence
Beta test: 35% of users adopted (70 of 200 users)
## Likelihoods
If true adoption is >20%:
- P(seeing 35% in beta | adoption >20%) = 75% (likely to see high beta if true)
If true adoption is ≤20%:
- P(seeing 35% in beta | adoption ≤20%) = 15% (unlikely to see high beta if false)
## Bayesian Update
Posterior = (75% × 60%) / [(75% × 60%) + (15% × 40%)]
Posterior = 45% / (45% + 6%) = 88%
## Conclusion
Updated belief: 88% confident adoption will exceed 20%
Evidence strongly supports launch, but not certain.
Clarify hypothesis (specific, testable claim), probability to estimate, timeframe (when outcome is known), success criteria, and why this matters (what decision depends on it). Example: "Product feature will achieve >20% adoption within 3 months" - matters for launch decision.
Step 2: Establish prior beliefs
Set initial probability using base rates (general frequency), reference class (similar situations), specific differences, and explicit probability assignment with justification. Good priors are based on base rates, account for differences, honest about uncertainty, and include ranges if unsure (e.g., 40-60%). Avoid purely intuitive priors, ignoring base rates, or extreme values without justification.
Step 3: Identify evidence and likelihoods
Assess evidence (specific observation/data), diagnostic power (does it distinguish hypotheses?), P(E|H) (probability if hypothesis TRUE), P(E|¬H) (probability if FALSE), and calculate likelihood ratio = P(E|H) / P(E|¬H). LR > 10 = very strong evidence, 3-10 = moderate, 1-3 = weak, ≈1 = not diagnostic, <1 = evidence against.
Step 4: Calculate posterior
Apply Bayes' Theorem: P(H|E) = [P(E|H) × P(H)] / P(E), or use odds form: Posterior Odds = Prior Odds × Likelihood Ratio. Calculate P(E) = P(E|H)×P(H) + P(E|¬H)×P(¬H), get posterior probability, and interpret change. For simple cases → Use resources/template.md calculator. For complex cases (multiple hypotheses) → Study resources/methodology.md.
Step 5: Calibrate and document
Check calibration (over/underconfident?), validate assumptions (are likelihoods reasonable?), perform sensitivity analysis, create bayesian-reasoning-calibration.md, and note limitations. Self-check using resources/evaluators/rubric_bayesian_reasoning_calibration.json: verify prior based on base rates, likelihoods justified, evidence diagnostic (LR ≠ 1), calculation correct, posterior calibrated, assumptions stated, sensitivity noted. Minimum standard: Score ≥ 3.5.
Common Patterns
For forecasting:
Use base rates as starting point
Update incrementally as evidence arrives
Track forecast accuracy over time
Calibrate by comparing predictions to outcomes
For hypothesis testing:
State competing hypotheses explicitly
Calculate likelihood ratio for evidence
Update belief proportionally to evidence strength
Don't claim certainty unless LR is extreme
For risk assessment:
Consider multiple scenarios (not just binary)
Update risks as new data arrives
Use ranges when uncertain about likelihoods
Perform sensitivity analysis
For avoiding bias:
Force explicit priors (prevents anchoring to evidence)
Use reference classes (prevents ignoring base rates)
