C15. Warm-up and dependence

Topic: Markov chains, Gibbs sampling, and Metropolis–Hastings · more questions on this topic
‹ C14

Does discarding MCMC warm-up guarantee convergence or make the retained draws independent? Explain briefly.

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Definitions/notation. Warm-up (burn-in) is an initial segment discarded to reduce the influence of initialisation. Discarding it neither proves convergence nor removes serial dependence: even a chain at equilibrium generally has dependent successive states, so mixing and Monte Carlo precision still need assessment.