STATISTICS Correction for “Sequential Monte Carlo without likelihoods,” by S. A. Sisson, Y. Fan, and Mark M. Tanaka, which appeared in issue 6, February 6, 2007, of Proc Natl Acad Sci USA (104:1760–1765; first published January 30, 2007; 10.1073/pnas.0607208104).
The authors note the following: It has been brought to our attention that the algorithm introduced in our paper (ABC-PRC) can produce a biased posterior sample, most noticeably through underestimation in distributional tails. This result occurs as the likelihood ratio in the sequential Monte Carlo incremental weights is approximated by using two unbiased Monte Carlo estimates. One way to avoid a biased posterior sample in the ABC-PRC algorithm is to directly evaluate the importance sampling distribution using a near-optimal backwards kernel. Hence the need for the Monte Carlo estimate in the denominator of the likelihood ratio is circumvented, and an unbiased sampler is obtained. As such, a corrected ABC-PRC algorithm would be:
The authors thank C. Robert and G. W. Peters for constructive discussion.
