October 07, 2014
390

# 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.

October 07, 2014

## Transcript

6. ### Bayesian v. Frequentist A fundamental diﬀerence in philosophy …that usually

get you to similar results* *for simple problems

9. ### Related to our degree of belief / certainty Related to

the frequency of repeated events
10. ### Related to our degree of belief / certainty ↳ Bayesian

↳ Frequentist Related to the frequency of repeated events

12. ### “There is a 50% chance it will rain tomorrow” “If

we observe many tomorrows, 50% of the time it will rain” Bayesian Frequentist
13. ### “There is a 50% chance it will rain tomorrow” “If

we observe many tomorrows, 50% of the time it will rain” Bayesian Frequentist lolwut
14. ### Can be more expensive (computationally) Priors (ahhhhhhh) No way to

make decisions Why to not go Bayesian?

go Bayesian?

go Bayesian?

24. ### Priors In Bayesian inference, you always need to specify a

prior. ! Everyone brings prior information into modeling, you just make it explicit.
25. ### Priors They mathematically specify your personal or subjective beliefs. They

tend not to matter with enough data
26. ### Priors They mathematically specify your personal or subjective beliefs. They

tend not to matter with enough data
27. ### Priors They mathematically specify your personal or subjective beliefs. They

tend not to matter with enough data
28. ### Priors They mathematically specify your personal or subjective beliefs. They

tend not to matter with enough data

31. ### Rules of thumb “Principle of transformation groups” Priors on location

parameters should be translation independent.
32. ### Rules of thumb “Principle of transformation groups” Priors on location

parameters should be translation independent.
33. ### Rules of thumb “Principle of transformation groups” Priors on location

parameters should be translation independent. Priors on scale parameters should be scale invariant.
34. ### DO NOT look at your data, then assign a prior

based on the data.
35. ### DO NOT look at your data, then assign a prior

based on the data. DO NOT always use uniform (flat) priors.
36. ### 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…
37. ### Nuisance parameters We don’t care about it, but we must

account for it to properly model the data
38. ### Nuisance parameters We don’t care about it, but we must

account for it to properly model the data
39. ### Nuisance parameters We don’t care about it, but we must

account for it to properly model the data marginal posterior
40. ### You go to The Telescope™ and measure the flux from

a star with no variability. Example: Nuisance parameters

= c 10

49. ### You are at The Telescope™ and you compute that there

is a 40% chance of rain tonight. Wat do? Making decisions