R Tutorial: Bayesian Linear Regression

Want to learn more? Take the full course at https://learn.datacamp.com/courses/bayesian-regression-modeling-with-rstanarm at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Now that we've reviewed the characteristics of a frequentist regression, let's examine how to estimate that same regression using Bayesian methods. As we learned in the last lesson, if we want to make inferences about the actual values of parameters, p-values and frequentist regression fails us. Bayesian estimation is one solution to this problem. With Bayesian methods the likelihood that used for frequentist regression, and what's known as a prior, form a posterior distribution. The details of this process are beyond the scope of this course. The key point is that Bayesian methods sample from this posterior distribution, and we can then create summaries of the distributions to make parameter inferences. Using the summaries allows us to make inferences about what values parameters might take. To estimate Bayesian regression models in this course, we'll be using the rstanarm package. rstanarm is an interface to Stan, which is a programming language for Bayesian inference. The rstanarm package offers a high level interface with pre-written Stan scripts for common models, like linear regression. We can load rstanarm using the normal library command that we use to load all packages. We can then estimate a linear regression using the stan_glm function. Here, we estimate the same model that we estimated using the lm function. Normally, when using the stan_glm function, we would see a great deal of output that looks like this. This output mainly provides progress updates. However, the models we'll estimate in this course all estimate very quickly. Therefore, this output has been suppressed in the rest of the course. Just like a regression estimated with lm, we can look at a summary of a regression estimated with stan_glm. Using the sum