This article proposes a new method of construction of Markov chains with a given stationary distribution. 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 analyze; it could be more efficient than some related MCMC 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 difficult problems. Theoretical study and numerical comparisons with some other available MCMC techniques are made.
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