C11. Monte Carlo estimation

Topic: Markov chains, Gibbs sampling, and Metropolis–Hastings · more questions on this topic
‹ Question 16 C12 ›

What is a Monte Carlo estimate of \mathbb{E}_\pi[h(\Theta)], and what is Monte Carlo error?

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Definitions/notation. For a target distribution \pi and integrable function h, a Monte Carlo estimate is N^{-1}\sum_{t=1}^N h(\theta^{(t)}), using independent draws from \pi or suitable ergodic MCMC output. Monte Carlo error is the finite-simulation discrepancy from \mathbb{E}_\pi[h(\Theta)], not the posterior uncertainty about \Theta; its assessment must account for dependence when draws are correlated.