New Insights into Approximate Bayesian Computation

Gérard Biau (1, 2, 3, 4) , Frédéric Cérou (5) , Arnaud Guyader (5)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LSTA - Laboratoire de Statistique Théorique et Appliquée
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification
5 ASPI - Applications of interacting particle systems to statistics

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 a new interesting hybrid between a k-nearest neighbor and a kernel method.

Mots clés: Approximate Bayesian Computation; Nonparametric estimation; Conditional density estimation; Nearest neighbor methods; Mathematical statistics

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Gérard Biau, Frédéric Cérou, Arnaud Guyader. New Insights into Approximate Bayesian Computation. 2012. ⟨hal-00721164v1⟩