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Error bounds for computing the expectation by Markov chain Monte Carlo
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Daniel Rudolf
Published/Copyright:
October 20, 2010
Abstract
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l2-, l4- and l∞-norm of the function are proven. By the estimation the well-known asymptotical limit of the error is attained, i.e. our bounds are correct to first order as n → ∞. We discuss the dependence of the error on a burn-in of the Markov chain. Furthermore we suggest and justify a specific burn-in for optimizing the algorithm.
Keywords.: Markov chain Monte Carlo methods; Markov chain Monte Carlo; error bounds; explicit error bounds; burn-in; mixing time; eigenvalue
Received: 2009-09-25
Revised: 2010-09-08
Published Online: 2010-10-20
Published in Print: 2010-December
© de Gruyter 2010
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Keywords for this article
Markov chain Monte Carlo methods;
Markov chain Monte Carlo;
error bounds;
explicit error bounds;
burn-in;
mixing time;
eigenvalue
Articles in the same Issue
- Editiorial
- Random packing of hyperspheres and Marsaglia's parking lot test
- Diffusion in a nonhomogeneous medium: quasi-random walk on a lattice
- Improved Halton sequences and discrepancy bounds
- Generalizing Sudoku to three dimensions
- Adaptive integration and approximation over hyper-rectangular regions with applications to basket option pricing
- Exact simulation of Bessel diffusions
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- Stochastic iterative projection methods for large linear systems
- Increasing the number of inner replications of multifactor portfolio credit risk simulation in the t-copula model
- A genetic algorithm approach to estimate lower bounds of the star discrepancy
- Random and deterministic fragmentation models
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