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Bayesian Regression and Model Selection

Bayesian Regression and Model Selection

This course is part of Applied Bayesian Data Analysis Specialization

Instructor: Konstantinos Pelechrinis

Included with

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4 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Implement variational inference for scalable Bayesian analysis and determine when to prefer VI over MCMC methods.
Apply Gaussian Process Regression and Dirichlet Processes for flexible non-parametric modeling solutions.
Execute complete Bayesian workflows using PyMC3 from model specification through validation and diagnostics.
Build decision-theoretic models using loss functions for applications in sports analytics, healthcare, and business decision-making.

Skills you'll gain

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This course is part of the Applied Bayesian Data Analysis Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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Gain a foundational understanding of a subject or tool
Develop job-relevant skills with hands-on projects
Earn a shareable career certificate

There are 4 modules in this course

Master Bayesian modeling through Bayesian linear regression, generalized linear models, hierarchical models and model selection. This course will deepen your understanding of modeling techniques and the importance of the prior when contrasted with traditional frequentist modeling approaches. You will understand the benefits of hierarchical models and how they automatically identify the right amount of pooling between data to provide a balance between the complete and no pooling approaches. You will learn how to apply posterior predictive checks for model selection and understand the Occam’s razor principle. This course combines theoretical modeling foundations with hands-on implementations.

Module details

Welcome to Bayesian Regression and Model Selection! In this module, we will introduce the Bayesian linear regression. We will see how we can place priors on the coefficients of the models and what we can learn from their posteriors. We will also learn how to define and infer the posteriors of a Bayesian linear regression with pymc.

What's included

5 videos7 readings5 assignments1 ungraded lab

5 videosTotal 18 minutes

Bayesian Models4 minutes
Bayesian Linear Regression3 minutes
Bayesian Linear Regression in pymc4 minutes
The choice of prior4 minutes
Multiple predictors and interactions3 minutes

7 readingsTotal 90 minutes

Course Overview10 minutes
Technical and Accessibility Support5 minutes
A brief review of modeling15 minutes
Other Bayesian Programming Tools10 minutes
Bayesian-vs-Frequentist Linear Regression30 minutes
Module Wrap-Up10 minutes
Recommended Learning Resources10 minutes

5 assignmentsTotal 85 minutes

Bayesian Linear Regression10 minutes
Lab Check-in: Bayesian linear regression in pymc5 minutes
The effect and importance of prior10 minutes
Test Yourself: Bayesian Regression - Simple and Multiple Linear Models30 minutes
Let's Practice: Bayesian Regression - Simple and Multiple Linear Models30 minutes

1 ungraded labTotal 60 minutes

Bayesian Linear Regression in pymc60 minutes

In this module, we will see how hierarchical models make it easy to deal with categorical data, especially when these data are nested. We will see how they automatically identify the right amount of pooling between data to provide a balance between the complete and no pooling approaches.

What's included

5 videos1 reading5 assignments1 ungraded lab

5 videosTotal 24 minutes

Hierarchical Models4 minutes
The Radon Model2 minutes
Complete, No, and, Partial Pooling11 minutes
Hierarchical Models3 minutes
Group-level information3 minutes

1 readingTotal 4 minutes

Module Wrap-Up4 minutes

5 assignmentsTotal 89 minutes

Approaches to Pooling12 minutes
Lab Check-in: BHM example at pymc5 minutes
Hierarchical models12 minutes
Test Yourself: Hierarchical Bayesian Models30 minutes
Let's Practice: Hierarchical Bayesian Models30 minutes

1 ungraded labTotal 120 minutes

BHM example at pymc120 minutes

In this module, we will extend the Bayesian linear regression to be able to deal with binary (categorical) and count data. We will see the Bernoulli likelihood for the Bayesian logistic regression and how we can extend it to more than two categories through the categorical likelihood. Finally, we will see the Bayesian Poisson regression (and other options) for count data.

What's included

3 videos5 readings4 assignments3 ungraded labs

3 videosTotal 10 minutes

Bayesian Logistic Regression4 minutes
Poisson regression3 minutes
Poisson regression example2 minutes

5 readingsTotal 72 minutes

Modeling Binary and Count Data with Bayesian GLMs20 minutes
Binary Data Example18 minutes
Modeling Multiclass Data with Bayesian Classification14 minutes
Other Distributions for Count Data15 minutes
Module Wrap-Up5 minutes

4 assignmentsTotal 82 minutes

Binary and categorical data12 minutes
Count data10 minutes
Test Yourself: Bayesian Logistic Regression and Generalized Linear Models (GLMs)30 minutes
Let's Practice: Bayesian Logistic Regression and Generalized Linear Models (GLMs)30 minutes

3 ungraded labsTotal 180 minutes

Logistic Rainfall60 minutes
Modeling Multiclass Data60 minutes
Poisson Bike Trips60 minutes

In this module, we will see the basic notions behind model selection and the philosophical and practical differences between frequentists and Bayesians on the topic. We will understand the difference between the posterior distribution of the model parameters and the posterior predictive distributions. The latter will lead us to the ideas of posterior predictive checks and model coverage.