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Stationarity preserving and efficiency increasing probability mass transfers made possible

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Abstract

We develop an efficient computational algorithm that produces efficient Markov chain Monte Carlo (MCMC) transition matrices. The first level of efficiency is measured in terms of the number of operations needed to produce the resulting matrix. The second level of efficiency is evaluated in terms of the asymptotic variance of the resulting MCMC estimators. Results are first given for transition matrices in finite state spaces and then extended to transition kernels in more general settings.

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Acknowledgment

we thank Pieter Omtzigt for the insight given in the construction of the first-degree optimal matrix that appears in Sect. 4 and for discussing earlier versions of the paper.

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Correspondence to Antonietta Mira.

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Financial support from F.A.R. 2006, University of Insubria and from the grant MIUR 2005 “Modelli marginali per variabili categoriche con applicazioni all’analisi causale” are gratefully acknowledged.

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Mira, A. Stationarity preserving and efficiency increasing probability mass transfers made possible. Computational Statistics 21, 509–522 (2006). https://doi.org/10.1007/s00180-006-0009-9

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