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”]