Bayesian methods are powerful tools for data science applications, complimenting traditional statistical and machine learning methods. Importantly, Bayesian models generate predictions and inferences that fully account for uncertainty. The main tool for conducting Bayesian analysis is Markov chain Monte Carlo (MCMC), a computationally-intensive numerical approach that allows a wide variety of models to be estimated. MCMC algorithms are available in several Python libraries, including PyMC3. I will teach users a practical, effective workflow for applying Bayesian statistics using MCMC via PyMC3 using real-world examples.

This tutorial is intended for analysts, data scientists and machine learning practitioners. Anyone looking for effective ways of making predictions and obtaining inference from datasets should find it useful. The material will assume an intermediate level of Python familiarity. Ideally, attendees should be familiar with Numpy and Jupyter. There is no expectation of students having a statistical background. Having completed the tutorial, students should be able to build basic Bayesian statistical models using their own data, validate those models, and interpret their output.

Introduction to PyMC3

• Gentle introduction to the PyMC3 API using a real example
• What is a Bayesian model?
  • Running example: comparison of one group with a continuous outcome to a threshold value
• How do we make a model Bayesian? - Mapping a model onto Bayes' formula
• Overview of the PyMC3 API
  • The PyMC3 Model
  • Probability distributions
  • Adding data to the model
  • Estimating the values of the variables
• Three steps of the Bayesian workflow

Coding Bayesian Models

• Challenge: how do we encode a Bayesian statistical model in PyMC3?
• This chapter will focus on Step 1 of the workflow
• Employ a slightly more sophisticated model: comparing 2 groups with continuous outcomes
  • Approach: start with original model, and see what needs to be changed in order to accomodate 2 groups
• How do we translate equations into code?
  • Relate each model component to Bayes' formula
• Picking your priors
  • Stochastic objects
• Transforming variables
  • Determinsitic objects
• Adding data via the likelihood function
  • Stochastic objects with observed values

Fitting Models with MCMC

• Challenge: how do we fit our PyMC3 model to our dataset?
• Why do we need MCMC?
  • Using simulation when problems cannot be solved analytically
• Overview of the Metropolis algorithm
  • Coding a simple MCMC algorithm by hand
    • Initializing variables
    • Proposing values for variables
    • Accepting or rejecting proposed values
    • Obtaining an estimate from the simulated values
• MCMC algorithms in PyMC3
  • Gradient-based MCMC
  • Using the sample function to fit your model

Checking your Model

• Challenge: how do we know if our model is any good, and what can we do if it isn't?
• How many samples do you need?
• Using convergence diagnostics to see if you're done
• What to do about autocorrelation
• Checking the fit of your model
• Reparameterizing your model to improve model performance

Summarizing and Interpreting Model Output

• Challenge: how do we obtain useful output from our model, such as predictions, estimates and plots?
• Extracting samples from the model trace
• Summarizing and exporting model output
• How to interpret what you have done
• Producing meaningful graphics
• Communicating your results to others