felipecustodio Overview & Purpose
Statistical Reasoning applies mathematical rigor to data interpretation, probability estimation, and decision making under uncertainty. It ensures that conclusions avoid common cognitive traps like base-rate neglect, sample size insensitivity, and regression to the mean.
When to Use
- Data Interpretation: Analyzing benchmark results, metric changes, or experiment outcomes.
- Bayesian Inference: Updating prior beliefs when new quantitative evidence arrives.
- Risk & Probability Modeling: Estimating odds of failure or success across probabilistic outcomes.
Execution Workflow
- State Prior Distribution ($P(A)$): Establish baseline probabilities based on historical data.
- Evaluate Likelihood ($P(B|A)$): Assess probability of observing the evidence given hypothesis $A$.
- Apply Bayes' Theorem: Calculate posterior probability $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$.
- Determine Confidence Interval: State margin of error and statistical significance level.
Expected Output Contract
### Statistical Assessment
- **Prior Probability P(A)**: [Baseline Rate]
- **Observed Likelihood P(B|A)**: [Evidence Probability]
- **Posterior Probability P(A|B)**: [Updated Rate]
- **Confidence Level**: [Significance Interval]
Scripts
scripts/statistical_reasoning.py- Deterministic evaluation, state validation, and CLI tool for statistical-reasoning.