On adaptive posterior concentration rates
By Marc Hoffmann, Judith Rousseau, Johannes Schmidt-Hieber. 2013
86 citations recorded by the source corpus.
tion of Holder balls and that moreover achieve our lower bound. We analyse the consequences in terms of asymptotic behaviour of poste- rior credible balls as well as frequentist minimax adaptive estimation. Our results are appended with an upper bound for the contraction rate under an arbitrary loss in a generic regular experiment. The up- per bound is attained for certain sieve priors and enables to extend our results to density estimation.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/54e519a4ed23efbc4ff661c92358774fd1e34957
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In Artificial Intelligence
- Kolyan Ray
- A. van der Vaart
- I. Castillo
- Yun Yang
- Anirban Bhattacharya
- Debdeep Pati
- Richard Nickl
- Johannes Schmidt-Hieber
In Statistics and Probability
- Kolyan Ray
- A. van der Vaart
- Judith Rousseau
- I. Castillo
- Richard Nickl
- Yun Yang
- Anirban Bhattacharya
- Debdeep Pati
Citations in the corpus
- Frequentist coverage and sup-norm convergence rate in Gaussian process regression (2017, background): “The Hellinger and total variation norms are by far the most common metrics for establishing posterior contraction rates and there is only a recent small literature for stronger norms [9, 22, 23, 53].”
- On Bayesian supremum norm contraction rates (2013, methodology): “In Gaussian white noise, adaptive results over Hölder classes are obtained in [19] for a class of sparse priors.”
- Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms (2017, unknown): “[25], [51], can fail to adapt to α0 ∧ α1 in the general case when α0 = α1 .”
- Adaptive Bernstein–von Mises theorems in Gaussian white noise (2014, background): “The assumptions in [24] ensure that prior draws are very sparse and only very few coefficients are fitted.”
- BAYESIAN LINEAR REGRESSION WITH SPARSE PRIORS (2014, background): “By adapting the lower bound argument in [17], Section 2, it follows that this is optimal.”