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Adaptive approximate Bayesian computation. (English) Zbl 1437.62393

Summary: Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in S. A. Sisson et al.’s [Proc. Natl. Acad. Sci. USA 104, No. 6, 1760–1765 (2007; Zbl 1160.65005)] partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of O. Cappé et al. [“Population Monte Carlo”, J. Comput. Graph. Stat. 13, No. 4, 907–929 (2004; doi:10.1198/106186004X12803)], and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 1160.65005

Software:

CAPP
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