Project 12: Bayesian Statistics Decision Lab

Build a Bayesian decision lab with prior sensitivity and posterior predictive checks.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 2 weeks
Main Programming Language Python
Alternative Programming Languages R, Stan ecosystem
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 2. The “Micro-SaaS / Pro Tool”
Prerequisites Projects 7, 9, 11
Key Topics Prior/likelihood/posterior, MAP vs MLE, credible intervals, Bayesian regression, MCMC concepts

1. Learning Objectives

  1. Build prior-to-posterior workflows for binary and continuous outcomes.
  2. Compare MAP and MLE interpretations.
  3. Produce credible intervals and posterior predictive checks.
  4. Perform prior sensitivity analysis for decision robustness.

2. All Theory Needed (Per-Concept Breakdown)

2.1 Bayesian Updating

  • Fundamentals: Posterior is prior updated by evidence.
  • Deep Dive into the concept: Conjugate forms teach intuition; non-conjugate cases require sampling and diagnostics.

2.2 Decision Under Posterior Uncertainty

  • Fundamentals: Decisions should use probability of practical improvement, not only point estimates.
  • Deep Dive into the concept: Posterior predictive checks test whether the model can generate data like what you observed.

3. Project Specification

3.1 What You Will Build

A Bayesian analysis CLI for campaign or product experiments with posterior decision thresholds.

3.2 Functional Requirements

  1. Prior and likelihood configuration for key scenarios.
  2. Posterior summary output (means, intervals, probabilities).
  3. MAP vs MLE comparison report.
  4. Prior sensitivity and posterior predictive diagnostics.

3.3 Non-Functional Requirements

  • Reproducible random seeds and sampler settings.
  • Clear uncertainty narrative in output memo.

3.4 Example Usage / Output

$ python bayesian_decision_lab.py --campaign spring_launch
P(variant_B > variant_A): 0.974
95% credible interval uplift: [0.003, 0.021]
Prior sensitivity: low
Posterior predictive check: pass

3.5 Real World Outcome

You ship decision-ready Bayesian summaries that communicate both upside probability and downside risk.

4. Solution Architecture

Config -> prior/likelihood module -> posterior engine -> diagnostics -> decision memo

5. Implementation Guide

5.1 Development Environment Setup

pip install numpy scipy pymc

5.2 Project Structure

P12/
  bayesian_decision_lab.py
  priors/
  outputs/

5.3 The Core Question You Are Answering

“Given prior knowledge and new evidence, what action has the best risk-adjusted payoff?”

5.4 Concepts You Must Understand First

  1. Bayes theorem and conjugacy
  2. MAP vs MLE
  3. Credible intervals
  4. Posterior predictive checks

5.5 Questions to Guide Your Design

  1. How will you justify prior choices?
  2. What posterior probability threshold triggers action?
  3. How will you detect sampler pathologies conceptually?

5.6 Thinking Exercise

Compare a skeptical and optimistic prior under the same data. Explain when both lead to the same decision.

5.7 The Interview Questions They’ll Ask

  1. How is Bayesian interval interpretation different from frequentist CI?
  2. Why does prior sensitivity matter?
  3. What does posterior predictive failure imply?
  4. When would MAP and MLE diverge meaningfully?
  5. What do MCMC diagnostics protect against?

5.8 Hints in Layers

  • Hint 1: Start with Beta-Binomial.
  • Hint 2: Add posterior decision probabilities.
  • Hint 3: Add non-conjugate extension.
  • Hint 4: Add predictive checks and sensitivity sweeps.

5.9 Books That Will Help

Topic Book Chapter
Bayesian fundamentals Statistical Rethinking Ch. 1-5
Hierarchical Bayes Bayesian Data Analysis hierarchical chapters
Practical Bayesian workflow project docs/notebooks selected

6. Testing Strategy

  • Closed-form conjugate test comparisons.
  • Prior sensitivity regression tests.
  • Posterior predictive sanity checks.

7. Common Pitfalls & Debugging

Pitfall Symptom Solution
Overconfident posterior too narrow intervals inspect likelihood/prior scale
Weak diagnostics false certainty add trace and effective-sample checks
Hidden prior assumptions stakeholder mistrust explicit prior rationale in memo

8. Extensions & Challenges

  • Add hierarchical Bayesian conversion model.
  • Add decision utility/loss function module.

9. Real-World Connections

  • Marketing optimization.
  • Adaptive experimentation and personalization.

10. Resources

  • Statistical Rethinking
  • Bayesian Data Analysis

11. Self-Assessment Checklist

  • I can explain posterior updates in plain language.
  • I can justify prior choices and sensitivity checks.
  • I can present Bayesian decision metrics to stakeholders.

12. Submission / Completion Criteria

Minimum: one conjugate workflow with posterior decision output.

Full: non-conjugate extension with predictive and sensitivity diagnostics.