Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Wentao Li, Paul Fearnhead; Convergence of regression-adjusted approximate Bayesian computation, Biometrika, Volume 105, Issue 2, 1 June 2018, Pages 301–318, https://doi.org/10.1093/biomet/asx081 is available online at: https://academic.oup.com/biomet/article/105/2/301/4827648
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Accepted author manuscript, 236 KB, PDF document
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Convergence of regression-adjusted approximate Bayesian computation
AU - Li, Wentao
AU - Fearnhead, Paul
N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Wentao Li, Paul Fearnhead; Convergence of regression-adjusted approximate Bayesian computation, Biometrika, Volume 105, Issue 2, 1 June 2018, Pages 301–318, https://doi.org/10.1093/biomet/asx081 is available online at: https://academic.oup.com/biomet/article/105/2/301/4827648
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We present asymptotic results for the regression-adjusted version of approximate Bayesiancomputation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth; one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.
AB - We present asymptotic results for the regression-adjusted version of approximate Bayesiancomputation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth; one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.
KW - approximate Bayesian computation
KW - Importance sampling
KW - Local-linear regression
KW - Partial information
U2 - 10.1093/biomet/asx081
DO - 10.1093/biomet/asx081
M3 - Journal article
VL - 105
SP - 301
EP - 318
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 2
ER -