However there are algorithms that do mimic the penalty method. In a recent paper with George Deligiannidis and Mike Pitt (http://arxiv.org/pdf/1511.04992v3), we have introduced the correlated pseudo-marginal algorithm which is a novel version of the pseudo-marginal algorithm correlating the estimators of the numerotor and denominator in the MH acceptance ratio.

We show in Section 4 of this paper that the correlated pseudo marginal algorithm converges weakly to the penalty method as the number of data T goes to infinity.

]]>In our paper GPS-ABC, we drew some inspiration from Ceperley and Dewing’s paper. Although we didn’t use the expected acceptance probabilty A in our algorithm, we could have by using the synthetic likelihood since the synthetic likelihood estimates the unknown variance term for us. We also minimized the MAD which required estimating the median rather than the mean acceptance.

There are probably a lot of new algorithms that can be derived from C&P paper, though the correction is fairly straightforward to derive.

Best,

Ted

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