RStanARM (http://mc-stan.org/interfaces/rstanarm.html) is a package for fitting Bayesian regression models. It allows us to fit Bayesian regression models using conventional R model syntax: To fit the usual "glm(...)" model, we just write "stan_glm(...)" with an added argument for priors. It's that easy. In this tutorial, I give a tour of the RStanARM package: fitting basic regression models, inspecting model results using the package's superb Shiny app, visualizing uncertainty by drawing from a posterior distribution, simulating new data using a posterior predictive distribution, regularizing models with strong priors, and comparing models using Leave-One-Out cross-validation. Knowledge of Bayesian statistics is not required; RStanARM is a great gateway into Bayesian statistics.
Tristan Mahr is a PhD candidate in Communication Sciences and Disorders at UW-Madison. He uses R to work on eye-tracking and speech perception data. @tjmahr, github.com/tjmahr.