• How to actual use Bayes in practice: Approximate Bayesian computation (as we did in part 1 and 2) is slow. Faster models all require that the generative model allows you to directly calculate the probability of seeing a particular result. Faster models also explore the parameter space in a smarter way.

• relates Bayes to maximum likelihood estimation

• I find the model at time 5:30 a bit confusing. My guess is that y is sampled from a normal distribution where the mean of the distribution is determined by intercept + slope * x and the stddev is held constant. So, to generate a y, you select an x, plug it into the line equation to get the mean, and then sample for the normal with the determined mean (and chosen stddev). Presumably, the sampling of the normal represents noise in the process.

• “Now this is a generative model, but it is not yet a Bayesian model. For that, we need to represent all uncertainty by probability, and add prior distributions over all parameters.

• Result of Bayesian linear regression gives you an idea of how likely the various parameters are to have generated the data.

• TODO: find another explanation of a Bayesian approach to linear regression.

• Markov Chain Monte Carlo (MCMC) allows for exploration of complicated parameter spaces. They walk around the parameter space and sample from the probability distributions. They will revisit and sample each parameter set in proportion to how likely it is (to have generated the data).

• Stan is a language for Bayesian modelling. You define your model in Stan and then it takes cares of fitting it.

• Things that can go wrong in MCMC: initial parameter values are way off, our algorithm doesn’t have enough time to explore the parameter space, algorithm gets stuck at a local maximum. Very similar to optimization.