Bounds on regeneration times and convergence rates for Markov chains
In many applications of Markov chains, and especially in Markov chain Monte Carlo algorithms, the rate of convergence of the chain is of critical importance. Most techniques to establish such rates require bounds on the distribution of the random regeneration time T that can be constructed, via splitting techniques, at times of return to a "small set" C satisfying a minorisation condition P(x,·)[greater-or-equal, slanted][var epsilon][phi](·), x[set membership, variant]C. Typically, however, it is much easier to get bounds on the time [tau]C of return to the small set itself, usually based on a geometric drift function , where . We develop a new relationship between T and [tau]C, and this gives a bound on the tail of T, based on [var epsilon],[lambda] and b, which is a strict improvement on existing results. When evaluating rates of convergence we see that our bound usually gives considerable numerical improvement on previous expressions.
Year of publication: |
1999
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Authors: | Roberts, G. O. ; Tweedie, R. L. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 80.1999, 2, p. 211-229
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Publisher: |
Elsevier |
Keywords: | Renewal times Geometric ergodicity Rates of convergence Markov chain Monte Carlo Shift coupling Computable bounds |
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