Approximate Bayesian Computation: a nonparametric perspective - Archive ouverte HAL Access content directly
Journal Articles Journal of the American Statistical Association Year : 2010

Approximate Bayesian Computation: a nonparametric perspective

(1)
1
Michael G B Blum
  • Function : Author
  • PersonId : 854172

Abstract

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s_obs from the data and simulating summary statistics for different values of the parameter theta. The posterior distribution is then approximated by an estimator of the conditional density g(theta|s_obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment and of the transformations of the summary statistics. Supplemental materials containing the details of the proofs are available online.
Fichier principal
Vignette du fichier
abcblum_jasaformat_v2.pdf (440.31 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00373301 , version 1 (03-04-2009)
hal-00373301 , version 2 (06-05-2009)
hal-00373301 , version 3 (13-05-2009)
hal-00373301 , version 4 (08-09-2009)
hal-00373301 , version 5 (08-04-2010)

Identifiers

Cite

Michael G B Blum. Approximate Bayesian Computation: a nonparametric perspective. Journal of the American Statistical Association, 2010, 105, pp.1178-1187. ⟨10.1198/jasa.2010.tm09448⟩. ⟨hal-00373301v5⟩
2135 View
286 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More