Statistics Graduate Level Quiz
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SIMULATION, RESAMPLING & COMPUTATION
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A stationary Markov chain is used to estimate Eπ[h(X)]E_\pi[h(X)]. Under the stationary distribution, Var⁡π(h)=4\operatorname{Var}_\pi(h)=4, and the lag-kk autocorrelation of h(Xt)h(X_t) is ρk=0.5k\rho_k=0.5^k. The usual large-sample Markov chain variance approximation is assumed.
Approximately how many post-burn-in iterations are needed for the Monte Carlo standard error of the sample mean to be at most 0.020.02?
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