McElreath: A Bayesian approach to hierarchical modeling, using R to build our own estimator from scratch

CPB workshop continues, introduction to Bayesian inference.

McElreath discusses (slides):

• Bayes Theorem

$$P(\theta | D) = \frac{Pr(D|\theta) Pr(\theta )}{Pr(D)}$$

• Philosophy of Priors, Uninformative Priors

• Confidence intervals / credible intervals for free

• Computing the posterior: Directly or by MCMC

Nice visual example of updating prior as we add data:

[gist id=“797795”]

• King Markov and the chain islands.

• Evaluating: Burn in , autocorrelation.  Thinning (saves memory).

• Metropolis2.R bad mixing.

• Compare better and worse proposal mechanisms, motivates Gibbs Sampling: propose from the posterior, always accepted.

Richard’s code:

[gist id=“797782”]