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Over-relaxation methods and coupled Markov chains for Monte Carlo simulation. (English) Zbl 1247.62134
Summary: This paper is concerned with improving the performance of certain Markov chain algorithms for Monte Carlo simulations. We propose a new algorithm for simulating from multivariate Gaussian densities. This algorithm combines ideas from coupled Markov chain methods and from an existing algorithm based only on over-relaxation. The rate of convergence of the proposed and existing algorithms can be measured in terms of the square of the spectral radius of certain matrices. We present examples in which the proposed algorithm converges faster than the existing algorithm and the Gibbs sampler. We also derive an expression for the asymptotic variance of any linear combination of the variables simulated by the proposed algorithm. We outline how the proposed algorithm can be extended to non-Gaussian densities.

62H10 Multivariate distribution of statistics
65C40 Numerical analysis or methods applied to Markov chains
65C10 Random number generation in numerical analysis
65C05 Monte Carlo methods
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