bayesian-reasoning-calibration

# Bayesian Reasoning & Calibration

## Table of Contents

- [Purpose](#purpose)
- [When to Use This Skill](#when-to-use-this-skill)
- [What is Bayesian Reasoning?](#what-is-bayesian-reasoning)
- [Workflow](#workflow)
  - [1. Define the Question](#1--define-the-question)
  - [2. Establish Prior Beliefs](#2--establish-prior-beliefs)
  - [3. Identify Evidence & Likelihoods](#3--identify-evidence--likelihoods)
  - [4. Calculate Posterior](#4--calculate-posterior)
  - [5. Calibrate & Document](#5--calibrate--document)
- [Common Patterns](#common-patterns)
- [Guardrails](#guardrails)
- [Quick Reference](#quick-reference)

## Purpose

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:**

```markdown
# Should we launch Feature X?

## Prior Belief
Be