Bayesian Seminar 16 October 2015 Norman Fenton Queen Mary University of London and Agena Ltd

1. Bayesian Networks why smart data is better than big data Bayesian Seminar 16 October 2015 Norman Fenton Queen Mary University of London and Agena Ltd

2. Outline From Bayes to Bayesian networks Why pure machine learning is insufficient Applications Way forward

3. From Bayes to Bayesian networks

4. We have a hypothesis H We get some evidence E E(Positive Test?) H (Person hasdisease?) Introducing Bayes 1 in a 1000 100% accurate for those with disease; 95% accurate for those without What is the probability a person has the disease if they test positive?

5. P(E|H)*P(H) P(E) P(E|H)*P(H) P(H|E) = = P(E|H)*P(H) + P(E|not H)*P(not H) 1*0.001 0.001  2% = P(H|E) 0.0196 = 1*0.001 + 0.05*0.999 0.5005 Bayes Theorem We have a prior P(H) = 0.001 Waste of time showing this to most people!!! We know the (likelihood) values for P(E|H) But we want the posterior P(H|E) =

6. Imagine 1,000 people

7. One has the disease

8. But about 5% of the remaining 999 peoplewithout the disease test positive. That is about 50 people

9. So about 1 out of 50 who testpositive actually have the disease That’s about 2% That’s very different fromthe 95% assumed by most medics

10. A more realistic scenario This is a Bayesian network Cause 1 Cause 2 Disease Z Disease Y Disease X Symptom 1 Test A Symptom 2 Test B The necessary Bayesian propagation calculations quickly become extremely complex

11. The usual big mistake Combined Hypothesis Combined Evidence/data

12. The Barry George case

13. The Barry George case Evidence George fired gun George fired gun

14. Late 1980s breakthrough Pearl Lauritzen and Spiegelhalter

15. A Classic BN

16. Marginals

17. Dyspnoea observed

18. Also non-smoker

19. Positive x-ray

20. ..but recent visit to Asia

21. How to develop complex models Can we really LEARN this kind of model from data?

22. How to develop complex models Definitional idiom Cause consequence idiom Induction idiom Measurement idiom Idioms

23. How to develop complex models Bayesian net objects

24. How to develop complex models Ranked nodes

25. Static discretisation: marginals

26. Dynamic discretisation: marginals

27. Static discretisation with observations

28. Dynamic discretisation with observations

29. Why pure machine learning is insufficient

30. A typical data-driven study

31. BN Model learnt purely from data Age Brain scanresult Injurytype Outcome Delay in arrival Arterialpressure Pupildilation

32. Regression model learnt purely from data Brain scanresult Injurytype Arterialpressure Delay in arrival Pupildilation Age Outcome

33. Expert causal BN with hidden explanatory and intervention variables Arterialpressure Injurytype Brain scanresult Delay in arrival Pupildilation Seriousnessof injury Age Ability torecover Treatment Outcome

34. Danger of pure data driven decision making: Example of a Bank database on loans

35. Other examples Massive databases cannot learn even tiny models The massive shadow cast by Simpson’s paradox See:www.probabilityandlawblogspot.co.uk

36. applications

37. Legal arguments and forensics

38. Football prediction overview

39. Parameter learning from past data

40. Game specific information

41. Taking account of fatigue

42. Incorporating recent match data

43. Final prediction

44. Final prediction www.pi-football.com Constantinou, A., N. E. Fenton and M. Neil (2013): "Profiting from an Inefficient Association Football Gambling Market: Prediction, Risk and Uncertainty Using Bayesian Networks". Knowledge-Based Systems. Vol 50, 60-86

45. Trauma Care Case Study • QM RIM Group • The Royal London Hospital • US Army Institute of Surgical Research

46. Improving on MESS Score method

47. Life Saving: Prediction of Physiological Disorders

48. Limb Saving: Prediction of Limb Viability

49. www.traumamodels.com