23.1 Understand the Stan computing paradigm - Video Tutorials & Practice Problems

<v Voiceover>As modern computers</v> become more and more powerful, Bayesian data analysis becomes more and more feasible. For many years, Bayesian analysis was considered slow because it had to generate thousands upon thousands of simulations. Though, new computers can easily generate these thousands of simulations. They have new Bayesian languages, such as Stan, you can get by with hundreds of simulations instead of thousands. So Bayesian data analysis is better now than it ever was before. Bayesian regression is rooted in Bayes' formula. This states that the posterior distribution of our parameters is equal to the likelihood times the prior over a normalizing constant. This can be simplified to the posterior is proportionate to the likelihood times the prior. And the way we find this posterior is through simulation. This is done through Markov chain Monte Carlo. In the past, a statistician might have needed to write their own MCMC sampler. Then, eventually they could use bugs or jags. Fortunately now, there is Stan, a new language out of Andy Gomez' group at Columbia University that makes doing Bayesian simulation easy and fast. And fortunately, it integrates nicely with R, as we will see.