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.

The prior model

Simulating a Beta prior

Comparing & contrasting Beta priors

Which prior?

Data & the likelihood

Simulating the dependence of X on p

Approximating the likelihood function

Interpreting the likelihood function

The posterior model

Define, compile, and simulate

Updating the posterior

Influence of the prior & data on the posterior

Introduction to Bayesian Modeling

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.

The Normal-Normal model

Normal-Normal priors

Sleep study data

Insights from the prior and data

Simulating the Normal-Normal in RJAGS

Define, compile, & simulate the Normal-Normal

Posterior insights on sleep deprivation

Markov chains

Storing Markov chains

Markov chain trace plots

Markov chain density plots

Markov chain diagnostics & reproducibility

Multiple chains

Naive standard errors

Reproducibility

Bayesian Models & Markov Chains

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.

A simple Bayesian regression model

Regression priors

Visualizing the regression priors

Weight & height data

Bayesian regression in RJAGS

Define, compile, & simulate the regression model

Regression Markov chains

Posterior estimation & inference

Posterior point estimates

Posterior credible intervals

Posterior probabilities

Posterior prediction

Inference for the posterior trend

Calculating posterior predictions

Posterior predictive distribution

Bayesian Inference & Prediction

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.

Bayesian regression with a categorical predictor

RailTrail sample data

RJAGS simulation with categorical variables

Interpreting categorical coefficients

Inference for volume by weekday

Multivariate Bayesian regression

Re-examining the RailTrail data

RJAGS simulation for multivariate regression

Interpreting multivariate regression parameters

Posterior inference for multivariate regression

Bayesian Poisson regression

RJAGS simulation for Poisson regression

Plotting the Poisson regression model

Inference for the Poisson rate parameter

Poisson posterior prediction

Conclusion

Multivariate & Generalized Linear Models

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.

Fundamentals of Bayesian Data Analysis in R

Introduction to the Tidyverse

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

Bayesian Modeling with RJAGS

Likely to Recommend

Reproducibility

“Bayesian Modeling with RJAGS”

Exercise instructions

Hands-on interactive exercise

Bayesian Modeling with RJAGS

Chapter 1: Introduction to Bayesian Modeling

Chapter 2: Bayesian Models & Markov Chains

Chapter 3: Bayesian Inference & Prediction

Chapter 4: Multivariate & Generalized Linear Models

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