1. Conclusion
Bayesian estimation of regressions models with rstanarm offers one solution to problem presented by inferences made with frequentist regression. I hope you have enjoyed this course and learning about how to implement a Bayesian model on your own.
2. What we've learned
In this course you've learned how to complete a Bayesian regression analysis from beginning to end. We started by learning how to estimate a Bayesian regression model, including the differences from a frequentist regression, and how Bayesian methods allow us to make inferences about the actual parameter values. We then explored how we can modify a Bayesian model by altering the size of our posterior distribution, changing priors, and altering the estimation algorithm.
3. What we've learned
We then learned about how to evaluate the fit of our model using the R-squared statistic, posterior predictive model checks, and model comparison. Finally, we looked how we can use our estimated model to make predictions and visualizations to communicate our results.
4. What we've missed
We've covered a lot in this course, but there is much more to learn. There are many topics that are important for Bayesian inference that we touched on, but were beyond the scope of this course. For example, the mathematics of posterior distribution calculations and LOO approximations, how to choose the best prior distribution, and the causes of estimation errors in the sampling algorithm. Andrew Gelman's *Bayesian Data Analysis* gives a good overview of most of these topics. Information on the LOO approximation can be found in the documentation for the LOO package, along with accompanying resources and research articles. Finally, the Stan documentation and reference manual gives more details about the sampling algorithm, and how errors can arise.
5. What comes next?
This was just the beginning of Bayesian modeling. If you want to learn more, I encourage you to check out the other Bayesian data analysis courses here on DataCamp. In addition, the rstanarm website has many resources for estimating all different types of regression model including Poisson and logistic regression, and multi-level models. Finally, if you are interested in the more technical aspects of Bayesian estimation, I would highly recommend the Bayesian Data Analysis book by Andrew Gelman and his colleagues that we mentioned previously.
6. Thank you!
Thank you for following along with this course. I hope you continue to learn about Bayesian modeling and use it in your own work!