The document discusses combining intuition and data using Bayesian probability and statistics. It argues that intuition and data should both be used together rather than separately, as each alone can lead to incorrect conclusions. Bayesian probability provides a framework to combine both sources of information systematically. The impact of subjective priors fades as more objective data is obtained.

1. Combining Intuition and Data
John D. Cook
Singular Value Consulting
September 11, 2014
John D. Cook Singular Value Consulting Combining Intuition and Data

2. Why combine intuition and data?
John D. Cook Singular Value Consulting Combining Intuition and Data

3. Why combine intuition and data?
Either one alone can lead to nonsense.
John D. Cook Singular Value Consulting Combining Intuition and Data

4. Why combine intuition and data?
Either one alone can lead to nonsense.
It's not really possible to separate them.
John D. Cook Singular Value Consulting Combining Intuition and Data

5. Why combine intuition and data?
Either one alone can lead to nonsense.
It's not really possible to separate them.
Better to be explicit about it.
John D. Cook Singular Value Consulting Combining Intuition and Data

6. Consistency rules for quantifying belief
John D. Cook Singular Value Consulting Combining Intuition and Data

7. Consistency rules for quantifying belief
Bigger numbers correspond to stronger beliefs.
John D. Cook Singular Value Consulting Combining Intuition and Data

8. Consistency rules for quantifying belief
Bigger numbers correspond to stronger beliefs.
If you can calculate a conclusion two ways,
both must give the same answer.
John D. Cook Singular Value Consulting Combining Intuition and Data

9. Consistency rules for quantifying belief
Bigger numbers correspond to stronger beliefs.
If you can calculate a conclusion two ways,
both must give the same answer.
You must use all evidence.
John D. Cook Singular Value Consulting Combining Intuition and Data

10. Consistency rules for quantifying belief
Bigger numbers correspond to stronger beliefs.
If you can calculate a conclusion two ways,
both must give the same answer.
You must use all evidence.
If evidence increases your belief that A is true,
the same evidence must decrease your belief that A is false.
John D. Cook Singular Value Consulting Combining Intuition and Data

11. Consistency rules for quantifying belief
Bigger numbers correspond to stronger beliefs.
If you can calculate a conclusion two ways,
both must give the same answer.
You must use all evidence.
If evidence increases your belief that A is true,
the same evidence must decrease your belief that A is false.
If new evidence increases your belief in A,
but does not change your belief in B,
it must increase your belief in AB.
John D. Cook Singular Value Consulting Combining Intuition and Data

12. It's all probability
John D. Cook Singular Value Consulting Combining Intuition and Data

13. It's all probability
Plausibility of A
Degree of belief in A
Probability of A
P(A)
John D. Cook Singular Value Consulting Combining Intuition and Data

14. Learning
John D. Cook Singular Value Consulting Combining Intuition and Data

15. Learning
Learning in any order leads to the same place.
John D. Cook Singular Value Consulting Combining Intuition and Data

16. Learning
Learning in any order leads to the same place.
P(AB j C) = P(A j C) P(B j AC) = P(B j C) P(A j BC)
John D. Cook Singular Value Consulting Combining Intuition and Data

17. Learning
Learning in any order leads to the same place.
P(AB j C) = P(A j C) P(B j AC) = P(B j C) P(A j BC)
This is essentially Bayes theorem.
John D. Cook Singular Value Consulting Combining Intuition and Data

18. From Bayes theorem to Bayesian Statistics
John D. Cook Singular Value Consulting Combining Intuition and Data

19. From Bayes theorem to Bayesian Statistics
Create a model of what you want to study.
John D. Cook Singular Value Consulting Combining Intuition and Data

20. From Bayes theorem to Bayesian Statistics
Create a model of what you want to study.
Let be the parameter(s).
John D. Cook Singular Value Consulting Combining Intuition and Data

21. From Bayes theorem to Bayesian Statistics
Create a model of what you want to study.
Let be the parameter(s).
P( j data) / P(data j ) P()
John D. Cook Singular Value Consulting Combining Intuition and Data

22. Priors
John D. Cook Singular Value Consulting Combining Intuition and Data

23. Priors
You must start with a prior.
John D. Cook Singular Value Consulting Combining Intuition and Data

24. Priors
You must start with a prior.
You always know something before you collect data.
John D. Cook Singular Value Consulting Combining Intuition and Data

25. Priors
You must start with a prior.
You always know something before you collect data.
It's not necessary, or possible, to be completely precise.
John D. Cook Singular Value Consulting Combining Intuition and Data

26. The magic of Bayes
John D. Cook Singular Value Consulting Combining Intuition and Data

27. The magic of Bayes
Use everything you know, intuition and data.
John D. Cook Singular Value Consulting Combining Intuition and Data

28. The magic of Bayes
Use everything you know, intuition and data.
The impact of the prior automatically fades as data arrive.
John D. Cook Singular Value Consulting Combining Intuition and Data

29. The magic of Bayes
Use everything you know, intuition and data.
The impact of the prior automatically fades as data arrive.
All inference follows the same framework. No adhockery.
John D. Cook Singular Value Consulting Combining Intuition and Data

30. The magic of Bayes
Use everything you know, intuition and data.
The impact of the prior automatically fades as data arrive.
All inference follows the same framework. No adhockery.
Results are easy to interpret.
John D. Cook Singular Value Consulting Combining Intuition and Data

31. Tiny data: Backgammon example
John D. Cook Singular Value Consulting Combining Intuition and Data

32. Tiny data: Backgammon example
Is an undefeated player better than one who has been
defeated?
John D. Cook Singular Value Consulting Combining Intuition and Data

33. Tiny data: Backgammon example
Is an undefeated player better than one who has been
defeated?
Two wins and no losses vs. 90 wins and 10 losses
John D. Cook Singular Value Consulting Combining Intuition and Data

34. Tiny data: Backgammon example
Is an undefeated player better than one who has been
defeated?
Two wins and no losses vs. 90 wins and 10 losses
John D. Cook Singular Value Consulting Combining Intuition and Data

35. Resources
John D. Cook Singular Value Consulting Combining Intuition and Data

36. Resources
Probability Theory: The Logic of Science by E. T. Jaynes
http://tinyurl.com/bayes-backgammon
Contact info: http://JohnDCook.com
John D. Cook Singular Value Consulting Combining Intuition and Data