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Self-regenerative Markov chain Monte Carlo with adaptation. (English) Zbl 1044.62033

Summary: A new method of construction of Markov chains with a given stationary distribution is proposed. The method is based on constructing an auxiliary chain with some other stationary distribution and picking elements of this auxiliary chain a suitable number of times. The proposed method is easy to implement and analyse; it may be more efficient than other related Markov chain Monte Carlo techniques. The main attractive feature of the associated Markov chain is that it regenerates whenever it accepts a new proposed point. This makes the algorithm easy to adapt and tune for practical problems. A theoretical study and numerical comparisons with some other available Markov chain Monte Carlo techniques are presented.

MSC:

62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
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