Une introduction au critère BIC : fondements théoriques et interprétation
Journal de la société française de statistique, Volume 147 (2006) no. 1, p. 39-57
@article{JSFS_2006__147_1_39_0,
     author = {Lebarbier, \'Emilie and Mary-Huard, Tristan},
     title = {Une introduction au crit\`ere BIC : fondements th\'eoriques et interpr\'etation},
     journal = {Journal de la soci\'et\'e fran\c caise de statistique},
     publisher = {Soci\'et\'e fran\c caise de statistique},
     volume = {147},
     number = {1},
     year = {2006},
     pages = {39-57},
     language = {fr},
     url = {http://www.numdam.org/item/JSFS_2006__147_1_39_0}
}
Lebarbier, Émilie; Mary-Huard, Tristan. Une introduction au critère BIC : fondements théoriques et interprétation. Journal de la société française de statistique, Volume 147 (2006) no. 1, pp. 39-57. http://www.numdam.org/item/JSFS_2006__147_1_39_0/

Akaike H.(1973). Information theory as an extension of the maximum likelihood principle. In B.N. Petrov et F. Csaki(Eds.), Second International Symposium on Information Theory, pp. 267-281. Akademiai Kiado, Budapest. | MR 483125 | Zbl 0283.62006

Azaïs J.-M., E. Gassiat, et C. Mercadier(2003). Asymptotic distribution and power of the likelihood ratio test for mixtures : bounded and unbounded case. Technical report, Preprint, Orsay. | MR 2265342 | Zbl 1134.62010

Biernacki C., G. Celeux, et G. Govaert(2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on pattern analysis and machine intelligence 22(7), 719-725.

Birgé L. et P. Massart(2001). Gaussian model selection. J. Eur. Math. Soc. 3, 203-268. | MR 1848946 | Zbl 1037.62001

Bozdogan H.(1987). Model selection and Akaike's information criterion(AIC) : the general theory and its analytical extensions. Psychometrika 52, 345-370. | MR 914460 | Zbl 0627.62005

Burnham K.P. et D. Anderson(2002). Model selection and multi-model inference. Springer-Verlag New York. | MR 1919620 | Zbl 1005.62007

Castellan G.(1999). Modified Akaike's criterion for histogram density estimation. Technical Report 61, Universite Paris XI.

Celeux G. et G. Soromenho(1996). An entropy criterion for assessing the number of clusters in a mixture model. Classification Journal 13, 195-212. | MR 1421665 | Zbl 0861.62051

Chernoff H. et E. Lander(1995). Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial. Journal of Statistical Planning and Inference 43(1), 19-40. | MR 1314126 | Zbl 0812.62015

Csiszar I. et P.C. Shields(2000). The consistency of the bic markov order estimator. Ann. Statist. 28(6), 1601-1619. | MR 1835033 | Zbl 1105.62311

Dacunha-Castelle D. et E. Gassiat(1997). The estimation of the order of a mixture model. Bernoulli Journal of Mathematical Statistics and Probability 3(3), 279-299. | MR 1468306 | Zbl 0889.62012

Dudley R.M. et D. Haughton(1997). Information criteria for multiple data sets and restricted parameters. Statistica Sinica, 265-284. | MR 1466683 | Zbl 1030.62508

Dudley R.M. et D. Haughton(2002). Asymptotic normality with small relative errors of posterior probabilities of half-spaces. Ann. Statist. 30(5), 1311-1344. | MR 1936321 | Zbl 1014.62031

Fraley C. et A. E. Raftery(1998). How many clusters? which clustering method? answer via model-based cluster analysis. The Computer Journal 4 1, 578-588. | Zbl 0920.68038

Hannan E.J.(1980). The estimation of the order of an arma process. Ann. Statist. 8, 1071-1081. | MR 585705 | Zbl 0451.62068

Hartigan(1985). A failure of likelihood ratio asymptotics for normal mixtures. In Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer.

Haughton D.M.A.(1988). On the choice of a model to fit data from an exponentiel family. Ann. Statist. 16(1), 342-355. | MR 924875 | Zbl 0657.62037

Hoeting J.A., D. Madigan, A.E. Raftery, et C.T. Volinsky(1999). Bayesian model averaging : A tutorial. Statist. Science 14(4), 382-417. | MR 1765176 | Zbl 1059.62525

Hurvich C.M. et C.L. Tsai(1989). Regression and time series model selection in small samples. Biometrika 76, 297-307. | MR 1016020 | Zbl 0669.62085

Kass R.E. et L.A. Wasserman(1996). The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 90, 1343-1370. | Zbl 0884.62007

Kass R. E. et A. E. Raftery(1995). Bayes factors. J. Amer. Statist. Assoc. 90, 773-795. | Zbl 0846.62028

Kass R. E. et L. Wasserman(1995). A reference bayesian test for nested hypotheses and its relationship to the schwarz criterion. J. Amer. Statist. Assoc. 90(2), 928-934. | MR 1354008 | Zbl 0851.62020

Keribin C.(1998). Consistent estimate of the order of mixture models. Comptes Rendus de 1 Académie des Sciences 326, 243-248. | MR 1646973 | Zbl 0954.62023

Lebarbier E.(2005). Detecting multiple change-points in the mean of gaussian process by model selection. Signal processing 85, 717-736. | Zbl 1148.94403

Madigan D. et A.E. Raftery(1994). Model selection and accounting for model uncertainty in graphical models using Occam's window. J. Amer. Statist. Assoc. 89, 1535-1546. | Zbl 0814.62030

Mallows C.L.(1974). Some comments on Cp. Technometrics 15, 661-675. | Zbl 0269.62061

Mclachlan G. et D. Peel(2000). Finite Mixture Models. Wiley Series in Probability and Statistics. | MR 1789474 | Zbl 0963.62061

Poskitt D. S.(1987). Precision, complexity and bayesian model determination. J. R. Statist. Soc. B 49(2), 199-208. | MR 905191 | Zbl 0624.62010

Raftery A. E.(1995). Bayesian model selection in social research(with discussion). Sociological Methodology, 111-196.

Reschenhoffer E.(1996). Prediction with vague prior knowledge. Comm. Statist. 25, 601-608. | MR 1381061 | Zbl 0875.62129

Ripley B.D.(1995). Pattern Recognition and Neural Networks. Cambridge University Press. | MR 1438788 | Zbl 0853.62046

Rissanen J.(1978). Modelling by the shortest data description. Automatica 14, 465-471. | Zbl 0418.93079

Rissanen J.(1987). Stochastic complexity. J. R. Statist. Soc. B 49, 223-239. | MR 928936 | Zbl 0654.62008

Ronchetti(1985). Robust model selection in regression. Statis. Probab. Lett. 3, 21-23. | MR 784761

Schwarz G.(1978). Estimating the dimension of a model. Ann. Statist. 6, 461-464. | MR 468014 | Zbl 0379.62005

Shi P. et C.L. Tsai(1998). A note on the unification of the Akaike information criterion. J. R. Statist. Soc. B 60, 551-558. | MR 1625946 | Zbl 0909.62074

Sugiura(1978). Further analysis of the data by akaike's information criterion and the finite corrections. Comm. Statist. A7, 13-26. | Zbl 0382.62060

Tierney L. et J.B. Kadane(1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81, 33-59. | MR 830567 | Zbl 0587.62067

Van Der Vaart A.W.(1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. | Zbl 0910.62001