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

Leisen Fabrizio () and Mira Antonietta ()
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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

Economics and Quantitative Methods from Department of Economics, University of Insubria

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.

Pages: 14 pages
Date: 2006-07
New Economics Papers: this item is included in nep-dev, nep-fdg and nep-hpe
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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf06011

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