1. An Introduction to Bayesian Inference Michael Betancourt April 8, 2009 8.882

2. Text Introduction to Bayesian Inference An Example

3. Text Introduction to Bayesian Inference The General Problem

4. Text Introduction to Bayesian Inference Estimators

5. Text Introduction to Bayesian Inference Estimators: An Example

6. Text Introduction to Bayesian Inference Estimators: The Danger

7. Text Introduction to Bayesian Inference Estimators: The Limitation

8. Text Introduction to Bayesian Inference Maximum Likelihood

9. Text Introduction to Bayesian Inference Maximum Log Likelihood

10. Text Introduction to Bayesian Inference Minimization

11. Text Introduction to Bayesian Inference Maximum Likelihood: An Example

12. Text Introduction to Bayesian Inference Maximum Likelihood Biases

13. Text Introduction to Bayesian Inference Maximum Likelihood Subtleties

14. Text Introduction to Bayesian Inference Bimodal Distributions

15. Text Introduction to Bayesian Inference Back to the Drawing Board

16. Text Introduction to Bayesian Inference Bayes Theorem

17. Text Introduction to Bayesian Inference A New Approach? The are not random variables!

18. Text Introduction to Bayesian Inference Frequentist Statistics

19. Text Introduction to Bayesian Inference Uncertainty of Belief

20. Text Introduction to Bayesian Inference ‣ Axiom One ‣ Axiom Two The Cox Axioms

21. Text Introduction to Bayesian Inference A New Approach!

22. Text Introduction to Bayesian Inference Selecting Priors

23. Text Introduction to Bayesian Inference Selecting Priors

24. Text Introduction to Bayesian Inference An Example

25. Text Introduction to Bayesian Inference An Example

26. Text Introduction to Bayesian Inference An Example Revisted

27. Text Introduction to Bayesian Inference Marginalization

28. Text Introduction to Bayesian Inference Marginalization: An Example

29. Text Introduction to Bayesian Inference Marginalization: An Example

30. Text Introduction to Bayesian Inference Frequentist vs. Bayesian

31. Text Introduction to Bayesian Inference Bayesian Inference in Practice Frequentist ➲ Bayesian Optimization ➲ Expectation (Differentiation) ➲ (Integration)

32. Text Introduction to Bayesian Inference The Opposition ‣ “Priors are Subjective, Science Isn’t”

33. Text Introduction to Bayesian Inference Application: Model Selection

34. Text Introduction to Bayesian Inference Application: Model Selection

35. Text Introduction to Bayesian Inference Application: Model Selection

36. Text Introduction to Bayesian Inference The Bayesian Razor

37. Text Introduction to Bayesian Inference Application: Systematics Energy Scale5% Background Subtraction1% Trigger Bias2% Luminosity4%...n% Total7%

38. Text Introduction to Bayesian Inference Application: Systematics

39. Text Introduction to Bayesian Inference Application: Nonparametric Estimation

40. Text Introduction to Bayesian Inference Further Reading ‣ Information Theory, Inference, and Learning Algorithms, ‣ MacKay, http://www.inference.phy.cam.ac.uk/mackay/itila/www.inference.phy.cam.ac.uk/mackay/itila/ ‣ Data Analysis, ‣ Sivia with Skilling, Oxford 2006 ‣ Lectures on Probability, Entropy, and Statistical Physics, ‣ Caticha, http://arxiv.org/abs/0808.0012v1http://arxiv.org/abs/0808.0012v1