Bayesian statistics

This is from a very introductory talk on Bayesian statistics to a mixed audience taking a course on "statistics and machine learning in astronomy." Much inspiration from various people including Jake Vanderplas and David Hogg.

Transcript

1. FREQUENTIST STATISTICS
2. BAYESIAN STATISTICS
3. BAYESIAN STATISTICS
4. Bayesian v. Frequentist
5. Bayesian v. Frequentist A fundamental difference in philosophy
6. Bayesian v. Frequentist A fundamental difference in philosophy …that usually get you to similar results* *for simple problems
7. YOU HOW DO DEFINE PROBABILITY?
9. Related to our degree of belief / certainty
10. Related to our degree of belief / certainty Related to the frequency of repeated events
11. Related to our degree of belief / certainty ↳ Bayesian ↳ Frequentist Related to the frequency of repeated events
13. “There is a 50% chance it will rain tomorrow” Bayesian
14. “There is a 50% chance it will rain tomorrow” “If we observe many tomorrows, 50% of the time it will rain” Bayesian Frequentist
15. “There is a 50% chance it will rain tomorrow” “If we observe many tomorrows, 50% of the time it will rain” Bayesian Frequentist lolwut
16. Can be more expensive (computationally) Priors (ahhhhhhh) No way to make decisions Why to not go Bayesian?
17. Prior information Nuisance parameters Hierarchical models Interpretation of uncertainty Why go Bayesian?
18. Prior information Nuisance parameters Hierarchical models Interpretation of uncertainty Why go Bayesian?
22. The controversy
23. The controversy
24. The controversy ya, s’ok Frequentist
25. The controversy ya, s’ok Frequentist
26. The controversy ya, s’ok wtf m8? Frequentist
27. The controversy ya, s’ok wtf m8? Frequentist
28. The controversy ya, s’ok wtf m8? Frequentist
29. Priors In Bayesian inference, you always need to specify a prior. ! Everyone brings prior information into modeling, you just make it explicit.
30. Priors They mathematically specify your personal or subjective beliefs. They tend not to matter with enough data
31. Priors They mathematically specify your personal or subjective beliefs. They tend not to matter with enough data
32. Priors They mathematically specify your personal or subjective beliefs. They tend not to matter with enough data
33. Priors They mathematically specify your personal or subjective beliefs. They tend not to matter with enough data
34. Rules of thumb
35. Rules of thumb “Principle of transformation groups”
36. Rules of thumb “Principle of transformation groups” Priors on location parameters should be translation independent.
37. Rules of thumb “Principle of transformation groups” Priors on location parameters should be translation independent.
38. Rules of thumb “Principle of transformation groups” Priors on location parameters should be translation independent. Priors on scale parameters should be scale invariant.
40. DO NOT look at your data, then assign a prior based on the data.
41. DO NOT look at your data, then assign a prior based on the data. DO NOT always use uniform (flat) priors.
42. DO NOT look at your data, then assign a prior based on the data. DO NOT always use uniform (flat) priors. DO NOT try to use conjugate priors, unless you are hardcore…
43. Nuisance parameters We don’t care about it, but we must account for it to properly model the data
44. Nuisance parameters We don’t care about it, but we must account for it to properly model the data
45. Nuisance parameters We don’t care about it, but we must account for it to properly model the data marginal posterior
46. You go to The Telescope™ and measure the flux from a star with no variability. Example: Nuisance parameters
47. Example: Nuisance parameters time, t flux, f yer model f = c 10
48. Example: Nuisance parameters
49. Example: Nuisance parameters WE SUCK
50. Example: Nuisance parameters
51. Example: Nuisance parameters but then…
52. Example: Nuisance parameters but then…
53. Example: Nuisance parameters The marginal posterior
55. WE SUCK… LESS?
56. You are at The Telescope™ and you compute that there is a 40% chance of rain tonight. Wat do? Making decisions
57. Bayesians do not produce point estimates!