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Abstract: In the thesis we take the split chain approach to analyzing Markov chains anduse it to establish fixed-width results for estimators obtained via Markovchain Monte Carlo procedures MCMC. Theoretical results include necessary andsufficient conditions in terms of regeneration for central limit theorems forergodic Markov chains and a regenerative proof of a CLT version for uniformlyergodic Markov chains with $E {\pi}f^2< \infty.$ To obtain asymptoticconfidence intervals for MCMC estimators, strongly consistent estimators of theasymptotic variance are essential. We relax assumptions required to obtain suchestimators. Moreover, under a drift condition, nonasymptotic fixed-widthresults for MCMC estimators for a general state space setting not necessarilycompact and not necessarily bounded target function $f$ are obtained. The lastchapter is devoted to the idea of adaptive Monte Carlo simulation and providesconvergence results and law of large numbers for adaptive procedures underpath-stability condition for transition kernels.



Author: Krzysztof Latuszynski

Source: https://arxiv.org/







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