Probabilistic Programming

A Brief introduction to

Probabilistic Programming and Python

EuroSciPy - University of Cambridge August 2015

peadarcoyle@googlemail.com

All opinions my own

Who am I?

I work as a Data Scientist for a large Telecommunications Company

Masters in Mathematics

Interned at Amazon

Was a consultant for a while

Occasional contributor to Pandas and other projects

Co-organizer of the Data Science Meetup in Luxembourg

Member of Royal Statistical Society and NumFOCUS

@springcoil

I studied Mathematics, and encountered in textbooks Bayesians
This is a hard area to do by pen and paper, and most integrals can't be solved in exact form
Thankfully there was an invention of Monte Carlo Simulations
These simulations are used to approximate your likelihood function

I wanted to do a model of the Six Nations last year.

I wanted to build an understandable model to predict the winner

Key Info: Inferring the 'strength' of each team.

We only have scoring data, which is noisy hence Bayesian Stats

1. I picked Gamma as a prior for all teams

2. I used a Hierarchical Model because I wanted home advantage to be stronger for stronger teams based

3. From this I was able to create a novel model based only on historical results and scoring intensity

4. I simulated the likelihood function using MCMC

The model incorrectly predicted that England would come out on top.
Ireland actually won by points difference of 6 points.
It really came down to the wire!
"Prediction is difficult especially about the future"
One of the problems is what we call 'over-shrinkage' and you can delve into the results to see what the errors are, my model was within the errors.
Hat tip: Thanks to Abraham Flaxman and the PyMC3 on helping me port this from PyMC2 to PyMC3