For Hackers
\
Cam Davidson-Pilon
camdp.com
10 second bio:
I'm an ex-fina
nce quant currently
doing data at
Your Highschool Stats != Bayesian Stats
wtf?
Stats is actually really cool!
Stats is taught in a way that turns many people off.
-
Most were taught frequentists statistics (p-value, Z-scores, tests)
- I want to talk about Bayesian statistics
Bayesian analysis relies heavily on data-visualizations, instead of confusing p-values and hypothesis testing.
Philosophy and Interpretation of
Bayesian Statistics
Prior Prior + data (Prior + data) + data
We start with prior beliefs, which can be thought of as opinions.
Examples of Prior beliefs
- Beliefs on Google stock price next month
- Researcher's prior opinion of experimental outcome
- Does my code have a bug in it?
- Coin flips: how much information do I have?
Hence probabilities are subjective!
Add data...
Given our prior, we can update our opinion (read: beliefs, probability), and produce a new opinion (read: new beliefs, new probability).
This new distribution is called the posterior.
Iterate
if more data is available
Prior + data Prior + data
Prior = new Posterior = new Posterior
Posterior becomes
new Prior
One more important
detail to stress about Bayesian
statistics
Frequentist vs Bayesian programming function
- Freqntist( "My code passed all X tests; is there a bug in it?") returns: "No"
- Bayesian("My code often has bugs. My code pass all X test; is there still a bug in it?") {"No": 0.8, "Yes":0.2}
Bayesian methods return a distribution over answers, not a single answer.
Frequentist methods are still awesome
1. Least Squares, LASSO, Survival Analysis, etc. are awesome frequentist tools.
2. For large amounts of data, the two methods converge to the same answer.
3. For small data sizes, the two methods diverge and Bayesian methods should be preferred.
When do we have small data sizes?
"Sample sizes are never large. If N is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions).
But once N is 'large enough,' you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.).
N is never enough because if it were 'enough' you'd already be on to the next problem for which you need more data."
- Dr. Andrew Gelman
Glorious A/B Testing
(Make IPython go now)
Discovering Changes in User Behaviour
(make IPython go now)
For Hackers
Future
Developments
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Future Developments
- pip install bayesian-methods-for-hackers
- Meta datasets
- Adapting to the new IPython 1.0 and PyMC 3.0
- physical copy?
Thanks!
=)
Bayesian Methods For Hackers
By Cam DP
Bayesian Methods For Hackers
Introducing slides for presentations on the open-source book Bayesian Methods for Hackers
