MCMC Sampling and Diagnostics
Run sampling, inspect chains, and interpret Rhat and ESS diagnostics.
What Is MCMC?
Markov Chain Monte Carlo (MCMC) is a family of algorithms for drawing samples from a probability distribution when direct sampling is impossible. In Bayesian statistics, MCMC samples from the posterior distribution P(parameters | data).
RStan implements the No-U-Turn Sampler (NUTS), a state-of-the-art MCMC algorithm.
A Simple Stan Model
A Stan model is a text block defining data types, parameters, and the log-posterior. The simplest model estimates the mean of a normal distribution with known variance.
# library(rstan)
#
# stan_code <- '
# data {
# int<lower=0> N;
# vector[N] y;
# }
# parameters {
# real mu;
# real<lower=0> sigma;
# }
# model {
# mu ~ normal(0, 10); // prior
# sigma ~ exponential(1); // prior
# y ~ normal(mu, sigma); // likelihood
# }
# 'All lessons in this course
- Introduction to Bayesian Thinking
- Writing Stan Models in R
- MCMC Sampling and Diagnostics
- Posterior Predictive Checks