Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator
By Judith Rousseau, Botond Szab'o. 2015
61 citations recorded by the source corpus.
We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First we characterize the set where the maximum marginal likelihood estimator is located with high probability. Then we provide oracle type of upper and lower bounds for the contraction rates of the empirical Bayes posterior. We also show that the hierarchical Bayes posterior achieves the same contraction rate as the maximum marginal likelihood empirical Bayes posterior. We demonstrate the applicability of our general results for various models and prior distributions by deriving upper and lower bounds for the contraction rates of the corresponding empirical and hierarchical Bayes posterior distributions.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b83645410c4b1478ef1e123647fb907278a60748
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In Artificial Intelligence
- Botond Szab'o
- Stéphanie van der Pas
- A. van der Vaart
- Judith Rousseau
- Kolyan Ray
- Richard Nickl
- Subhashis Ghosal
- Shahar Mendelson
In Statistics and Probability
- Botond Szab'o
- Stéphanie van der Pas
- A. van der Vaart
- Judith Rousseau
- Kolyan Ray
- Richard Nickl
- Shahar Mendelson
- Vladimir Koltchinskii
Citations in the corpus
- On the Frequentist Properties of Bayesian Nonparametric Methods (2016, unknown): “Rousseau and Szabò, 2015.”
- Adaptive posterior contraction rates for the horseshoe (2017, result): “It turns out that the “MMLE plug-in posterior distribution” closely mimics the hierarchical Bayes posterior distribution, as has been observed in other settings [29, 26].”