We derive the optimal proposal density for Approximate Bayesian Computation
(ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The
criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective
number of samples per parameter proposal. The optimal proposal density
represents the optimal trade-off between favoring high acceptance rate and
reducing the variance of the importance weights of accepted samples. We discuss
two convenient approximations of this proposal and show that the optimal
proposal density gives a significant boost in the expected sampling efficiency
compared to standard kernels that are in common use in the ABC literature,
especially as the number of parameters increases.
Description
[1808.06040] Optimal proposals for Approximate Bayesian Computation
%0 Generic
%1 alsing2018optimal
%A Alsing, Justin
%A Wandelt, Benjamin D.
%A Feeney, Stephen M.
%D 2018
%K statistics
%T Optimal proposals for Approximate Bayesian Computation
%U http://arxiv.org/abs/1808.06040
%X We derive the optimal proposal density for Approximate Bayesian Computation
(ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The
criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective
number of samples per parameter proposal. The optimal proposal density
represents the optimal trade-off between favoring high acceptance rate and
reducing the variance of the importance weights of accepted samples. We discuss
two convenient approximations of this proposal and show that the optimal
proposal density gives a significant boost in the expected sampling efficiency
compared to standard kernels that are in common use in the ABC literature,
especially as the number of parameters increases.
@misc{alsing2018optimal,
abstract = {We derive the optimal proposal density for Approximate Bayesian Computation
(ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The
criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective
number of samples per parameter proposal. The optimal proposal density
represents the optimal trade-off between favoring high acceptance rate and
reducing the variance of the importance weights of accepted samples. We discuss
two convenient approximations of this proposal and show that the optimal
proposal density gives a significant boost in the expected sampling efficiency
compared to standard kernels that are in common use in the ABC literature,
especially as the number of parameters increases.},
added-at = {2019-09-18T18:48:55.000+0200},
author = {Alsing, Justin and Wandelt, Benjamin D. and Feeney, Stephen M.},
biburl = {https://www.bibsonomy.org/bibtex/2a4d2e24f7aee9854c5c1ec61c4b6d6fe/cpankow},
description = {[1808.06040] Optimal proposals for Approximate Bayesian Computation},
interhash = {9bfb22932d01d5d6bc8c7b4809fd4ba0},
intrahash = {a4d2e24f7aee9854c5c1ec61c4b6d6fe},
keywords = {statistics},
note = {cite arxiv:1808.06040Comment: 14 pages, 6 figures},
timestamp = {2019-09-18T18:48:55.000+0200},
title = {Optimal proposals for Approximate Bayesian Computation},
url = {http://arxiv.org/abs/1808.06040},
year = 2018
}