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Coalescence time and second largest eigenvalue modulus in the monotone reversible case

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  • Leisen Fabrizio

    () (Università di Modena e Reggio Emilia, Dipartimento di Matematica, Modena, Italy)

  • Mira Antonietta

    () (Department of Economics, University of Insubria, Italy)

Abstract

If T is the coalescence time of the Propp and Wilson, perfect simulation algorithm, the aim of this paper is to show that T depends on the second largest eigenvalue modulus of the transition matrix of the underlying Markov chain. This gives a relationship between the ordering based on the speed of convergence to stationarity in total variation distance and the ordering defined in terms of speed of coalescence in perfect simulation. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.

Suggested Citation

  • Leisen Fabrizio & Mira Antonietta, 2006. "Coalescence time and second largest eigenvalue modulus in the monotone reversible case," Economics and Quantitative Methods qf06011, Department of Economics, University of Insubria.
  • Handle: RePEc:ins:quaeco:qf06011
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