Asymptotic behaviour of the posterior distribution in overfitted mixture models

By Judith Rousseau, Kerrie L. Mengersen. 2011

366 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/794764b8512867a903ef3368e5190d24a13d0add

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In Artificial Intelligence

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Citations in the corpus

A Bayesian information criterion for singular models (2013, methodology): “Although no general formulae for the coefficients λij have been obtained thus far, the analysis of Rousseau and Mengersen (2011), equations (5) and (6), yields the tighter bound λij λ̄ij 0:5 := 1 2 { 2j −1+ 1 2 .i− j/ } = i+3j 4 − 1 2 : .6:8/ For j = i−1, we have λ̄ij0:5 =λij = i− 54 but we do not e”
A note on the multiplicative gamma process (2016, background): “Early results are available in simple models (Rousseau and Mengersen, 2011), and it is an active area of research to extend these properties to more general scenarios.”
On posterior contraction of parameters and interpretability in Bayesian mixture modeling (2019, methodology): “Rousseau and Mengersen [43] provided an interesting result in this regard, which states that for overfitted mixtures with a suitable Dirichlet prior on the mixing weights p, assuming that an upper bound to the number of mixture component is given, in addition to a second-order type identifiability c”
On strong identifiability and convergence rates of parameter estimation in finite mixtures (2016, background): “Keywords and phrases: mixture models, strong identifiability, Wasserstein distances, minimax bounds, maximum likelihood estimation.”
Singularity, misspecification and the convergence rate of EM (2018, methodology): “Such a result is of practical interest, as methods that overfit the number of mixtures are often more feasible than methods that estimate the number of components and subsequently estimate the parameters conditionally [24].”
The expected demise of the Bayes factor (2015, methodology): “This approach is inspired from the consistency results of Rousseau and Mengersen (2011) on estimated overfitting mixtures, i.e., mixture models where the data is actually issued from a mixture distribution with a smaller number of components.”