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Bayesian Modeling with RJAGS

In this course, you'll learn how to implement more advanced Bayesian models using RJAGS.

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4 Hours15 Videos58 Exercises6,721 Learners

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Course Description

The Bayesian approach to statistics and machine learning is logical, flexible, and intuitive. In this course, you will engineer and analyze a family of foundational, generalizable Bayesian models. These range in scope from fundamental one-parameter models to intermediate multivariate & generalized linear regression models. The popularity of such Bayesian models has grown along with the availability of computing resources required for their implementation. You will utilize one of these resources - the rjags package in R. Combining the power of R with the JAGS (Just Another Gibbs Sampler) engine, rjags provides a framework for Bayesian modeling, inference, and prediction.
  1. 1

    Introduction to Bayesian Modeling

    Free

    Bayesian models combine prior insights with insights from observed data to form updated, posterior insights about a parameter. In this chapter, you will review these Bayesian concepts in the context of the foundational Beta-Binomial model for a proportion parameter. You will also learn how to use the rjags package to define, compile, and simulate this model in R.

    Play Chapter Now
    The prior model
    50 xp
    Simulating a Beta prior
    100 xp
    Comparing & contrasting Beta priors
    100 xp
    Which prior?
    50 xp
    Data & the likelihood
    50 xp
    Simulating the dependence of X on p
    100 xp
    Approximating the likelihood function
    100 xp
    Interpreting the likelihood function
    50 xp
    The posterior model
    50 xp
    Define, compile, and simulate
    100 xp
    Updating the posterior
    100 xp
    Influence of the prior & data on the posterior
    50 xp
  2. 2

    Bayesian Models & Markov Chains

    The two-parameter Normal-Normal Bayesian model provides a simple foundation for Normal regression models. In this chapter, you will engineer the Normal-Normal and define, compile, and simulate this model using rjags. You will also explore the magic of the Markov chain mechanics behind rjags simulation.

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    The Normal-Normal model
    50 xp
    Normal-Normal priors
    100 xp
    Sleep study data
    100 xp
    Insights from the prior and data
    50 xp
    Simulating the Normal-Normal in RJAGS
    50 xp
    Define, compile, & simulate the Normal-Normal
    100 xp
    Posterior insights on sleep deprivation
    50 xp
    Markov chains
    50 xp
    Storing Markov chains
    100 xp
    Markov chain trace plots
    100 xp
    Markov chain density plots
    100 xp
    Markov chain diagnostics & reproducibility
    50 xp
    Multiple chains
    100 xp
    Naive standard errors
    100 xp
    Reproducibility
    100 xp
  3. 3

    Bayesian Inference & Prediction

    In this chapter, you will extend the Normal-Normal model to a simple Bayesian regression model. Within this context, you will explore how to use rjags simulation output to conduct posterior inference. Specifically, you will construct posterior estimates of regression parameters using posterior means & credible intervals, you will test hypotheses using posterior probabilities, and you will construct posterior predictive distributions for new observations.

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    A simple Bayesian regression model
    50 xp
    Regression priors
    100 xp
    Visualizing the regression priors
    100 xp
    Weight & height data
    100 xp
    Bayesian regression in RJAGS
    50 xp
    Define, compile, & simulate the regression model
    100 xp
    Regression Markov chains
    50 xp
    Posterior estimation & inference
    50 xp
    Posterior point estimates
    100 xp
    Posterior credible intervals
    100 xp
    Posterior probabilities
    100 xp
    Posterior prediction
    50 xp
    Inference for the posterior trend
    100 xp
    Calculating posterior predictions
    100 xp
    Posterior predictive distribution
    100 xp
  4. 4

    Multivariate & Generalized Linear Models

    In this final chapter, you will generalize the simple Normal regression model for application in broader contexts. You will incorporate categorical predictors, engineer a multivariate regression model with two predictors, and finally extend this methodology to Poisson multivariate regression models for count variables.

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    Bayesian regression with a categorical predictor
    50 xp
    RailTrail sample data
    100 xp
    RJAGS simulation with categorical variables
    100 xp
    Interpreting categorical coefficients
    50 xp
    Inference for volume by weekday
    100 xp
    Multivariate Bayesian regression
    50 xp
    Re-examining the RailTrail data
    100 xp
    RJAGS simulation for multivariate regression
    100 xp
    Interpreting multivariate regression parameters
    50 xp
    Posterior inference for multivariate regression
    100 xp
    Bayesian Poisson regression
    50 xp
    RJAGS simulation for Poisson regression
    100 xp
    Plotting the Poisson regression model
    100 xp
    Inference for the Poisson rate parameter
    100 xp
    Poisson posterior prediction
    100 xp
    Conclusion
    50 xp

Datasets

Sleep study data

Collaborators

Chester Ismay
Nick Solomon
Eunkyung Park

Prerequisites

Fundamentals of Bayesian Data Analysis in RIntroduction to the Tidyverse
Alicia Johnson HeadshotAlicia Johnson

Associate Professor, Macalester College

Professor Johnson’s primary research interest is in Markov chain Monte Carlo (MCMC) methods. The focus of her research has been on the convergence rates of chains corresponding to MCMC algorithms on general state spaces. In addition, she enjoys the unlimited applications of statistics. As a consultant for a division of the Centers for Disease Control and Prevention and the University of Minnesota, she has collaborated on projects in entomology, forestry, primatology, public health, and others. In other words, her work in statistics allows her to keep learning a little about a lot!
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