Asymptotic behaviour of the posterior distribution in overfitted mixture models
Rousseau, Judith ; Mengersen, Kerrie
HAL, hal-00641475 / Harvested from HAL
Text on HAL
In this paper we study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components, a situation commonly referred to as overfitted mixture. We prove in particular that quite generally the posterior distribution has a stable and interesting behaviour, since it tends to empty the extra components. This stability is achieved under some restriction on the prior, which can be used as a guideline for choosing the prior. Some simulations are presented to illustrate this behaviour.
Publié le : 2011-07-05
Classification:  Asymptotic,  Bayesian,  mixture models,  overfitting,  posterior concentration,  [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],  [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] 
@article{hal-00641475,
     author = {Rousseau, Judith and Mengersen, Kerrie},
     title = {Asymptotic behaviour of the posterior distribution in overfitted mixture models},
     journal = {HAL},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00641475}
}

Rousseau, Judith; Mengersen, Kerrie. Asymptotic behaviour of the posterior distribution in overfitted mixture models. HAL, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/hal-00641475/