Day 1 Recap

How are beliefs about the world formalised?

• As probability distributions over the possible values that the parameter in question could take on.

How do different priors influence a model’s estimates?

• Models with uninformative priors learn more from the data than do models with informative priors.
• But as the amount of data grows, the influence of the prior wanes.

How do we interpret a posterior probability distribution?

• It tells us how probable each possible parameter value is, given the data and the priors.
• The 95% Credible Interval gives us the range in which the model is 95% certain that the true value lies.

How does the model find the posterior distribution?

• brms models use an algorithm called Markov Chain Monte Carlo to approximate the posterior by drawing many samples from it.

How do Bayesian models generate data?

• The likelihood’s parameter values can be sampled from the prior distributions.
• And then we sample from the likelihood to generate one data point.