New insights into Approximate Bayesian Computation

被引：40

作者：

Biau, Gerard ^{[1
]}

Cerou, Frederic ^{[2
,3
]}

Guyader, Arnaud ^{[4
,5
]}

机构：

[1] Univ Paris 06, Sorbonne Univ, F-75005 Paris, France

[2] INRIA Rennes Bretagne Atlantique, F-35042 Rennes, France

[3] IRMAR, F-35042 Rennes, France

[4] IRMAR, INRIA Rennes Bretagne Atantique, F-35043 Rennes, France

[5] Univ Rennes 2, F-35043 Rennes, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2015年 / 51卷 / 01期

关键词：

Approximate Bayesian Computation; Nonparametric estimation; Conditional density estimation; Nearest neighbor methods; Mathematical statistics; DENSITY-FUNCTION; MONTE-CARLO; CONVERGENCE;

D O I：

10.1214/13-AIHP590

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever suitable likelihoods are not available. In the present paper, we analyze the procedure from the point of view of k-nearest neighbor theory and explore the statistical properties of its outputs. We discuss in particular some asymptotic features of the genuine conditional density estimate associated with ABC, which is an interesting hybrid between a k-nearest neighbor and a kernel method.

引用

页码：376 / 403

页数：28

共 55 条

[1] ON BANDWIDTH VARIATION IN KERNEL ESTIMATES - A SQUARE ROOT LAW [J].