Chris Fonnesbeck - Probabilistic Python: An Introduction to Bayesian Modeling with PyMC

Chris Fonnesbeck presents:

Probabilistic Python: An Introduction to Bayesian Modeling with PyMC

Bayesian statistical methods offer a powerful set of tools to tackle a wide variety of data science problems. In addition, the Bayesian approach generates results that are easy to interpret and automatically account for uncertainty in quantities that we wish to estimate and predict. Historically, computational challenges have been a barrier, particularly to new users, but there now exists a mature set of probabilistic programming tools that are both capable and easy to learn. We will use the newest release of PyMC (version 4) in this tutorial, but the concepts and approaches that will be taught are portable to any probabilistic programming framework.

This tutorial is intended for practicing and aspiring data scientists and analysts looking to learn how to apply Bayesian statistics and probabilistic programming to their work. It will provide learners with a high-level understanding of Bayesian statistical methods and their potential for use in a variety of applications. They will also gain hands-on experience with applying these methods using PyMC, specifically including the specification, fitting and checking of models applied to a couple of real-world datasets.

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00:00 Welcome!
0:08 Introduction
1:19 Probabilistic programming
1:53 Stochastic language ”primitives”
3:06 Bayesian inference
3:27 What is Bayes?
3:57 Inverse probability
4:39 Why Bayes
5:13 The Bayes formula
4:21 Stochastic programs
6:51 Prior distribution
8:12 Likelihood function
8:29 Normal distribution
8:53 Binomial distribution
9:14 Poisson distribution
9:32 Infer values for latent variables
9:54 Posterior distribution
9:47 Probabilistic programming abstracts the inference procedure
10:56 Bayes by hand
12:18 Conjugacy
16:43 Probabilistic programming in Python
17:24 PyMC and its features
19:15 Question: Among the different probabilistic programming libraries, is there a difference in what they have to offer?
20:39 Question: How can one know which likelihood distribution to choose?
21:35 Question: Is there a methodology used to specify the likelihood distribution?
22:30 Example: Building models in PyMC
27:31 Stochastic and deterministic variables
37:11 Observed Random Variables
41:00 Question: To what extent are the features of PyMC supported if compiled in different backends?
41:47 Markov Chain Monte Carlo and Bayesian approximation
43:04 Markov chains
44:19 Reversible Markov chains
45:06 Metropolis sampling
48:00 Hamiltonian Monte Carlo
49:10 Hamiltonian dynamics
50:49 No U-turn Sampler (NUTS)
52:11 Question: How do you know the number of leap frog steps to take?
52:55 Example: Markov Chain Monte Carlo in PyMC
1:13:30 Divergences and how to deal with them
1:15:08 Bayesian Fraction of Missing Information
1:16:25 Potential Scale Reduction
1:17:57 Goodness of fit
1:22:40 Intuitive Bayes course
1:23:09 Question: Do bookmakers use PyMC or Bayesian methods?
1:23:53 Question: How does it work if you have different samplers for different variables?
1:25:09 Question: What route should one take in case of data with many discrete variables and many possible values?
1:25:39 Question: Is there a natural way to use PyMC over a cluster of CPUs?