Estimation des paramètres d’un mélange par échantillonnage bayésien. (Bayesian sampling estimation of mixtures). (French) Zbl 0711.62026

Diebolt, Jean; Robert, Christian

C. R. Acad. Sci., Paris, Sér. I 311, No. 10, 653-658 (1990).

Summary: A formal Bayesian approach is not computationally useful for mixture estimation. We introduce here two iterative approximation methods which simulate the posterior distribution and provide convergent estimators. These sampling techniques take advantage of the incomplete data structure of the models, as EM and SEM do. The theoretical results we state here guarantee the validity of these approximations. In addition, simulations show the potential superiority of the Bayesian approach.

MSC:

62F15	Bayesian inference
65C99	Probabilistic methods, stochastic differential equations

Keywords:

estimation of mixtures; Bayesian sampling; iterative approximation methods; posterior distribution; convergent estimators; incomplete data; EM; SEM; simulations