Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed)

Published

**Asymptotics of ABC.** / Fearnhead, Paul.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed)

Fearnhead, P 2018, Asymptotics of ABC. in S Sisson, Y Fan & M Beaumont (eds), *Handbook of Approximate Bayesian Computation .* CRC Press, pp. 269-288.

Fearnhead, P. (2018). Asymptotics of ABC. In S. Sisson, Y. Fan, & M. Beaumont (Eds.), *Handbook of Approximate Bayesian Computation *(pp. 269-288). CRC Press.

Fearnhead P. Asymptotics of ABC. In Sisson S, Fan Y, Beaumont M, editors, Handbook of Approximate Bayesian Computation . CRC Press. 2018. p. 269-288

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title = "Asymptotics of ABC",

abstract = "We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data? The results we review show that ABC can perform well in terms of point estimation, but standard implementations will over-estimate the uncertainty about the parameters. If we use the regression correction of Beaumont et al. then ABC can also accurately quantify this uncertainty. The theoretical results also have practical implications for how to implement ABC.",

keywords = "stat.ME, math.ST, stat.CO, stat.TH",

author = "Paul Fearnhead",

note = "This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M. Beaumont",

year = "2018",

language = "English",

isbn = "9781439881507",

pages = "269--288",

editor = "Scott Sisson and Yanan Fan and Mark Beaumont",

booktitle = "Handbook of Approximate Bayesian Computation",

publisher = "CRC Press",

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T1 - Asymptotics of ABC

AU - Fearnhead, Paul

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PY - 2018

Y1 - 2018

N2 - We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data? The results we review show that ABC can perform well in terms of point estimation, but standard implementations will over-estimate the uncertainty about the parameters. If we use the regression correction of Beaumont et al. then ABC can also accurately quantify this uncertainty. The theoretical results also have practical implications for how to implement ABC.

AB - We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data? The results we review show that ABC can perform well in terms of point estimation, but standard implementations will over-estimate the uncertainty about the parameters. If we use the regression correction of Beaumont et al. then ABC can also accurately quantify this uncertainty. The theoretical results also have practical implications for how to implement ABC.

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KW - math.ST

KW - stat.CO

KW - stat.TH

M3 - Chapter (peer-reviewed)

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EP - 288

BT - Handbook of Approximate Bayesian Computation

A2 - Sisson, Scott

A2 - Fan, Yanan

A2 - Beaumont, Mark

PB - CRC Press

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