Posterior concentration rates for infinite dimensional exponential families

By Vincent Rivoirard, Judith Rousseau. 2012

53 citations recorded by the source corpus.

In this paper we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models are not necessarily Gaussian

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/dfbe843cd0fec12eb3d466c6e007207356ad0ae5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. I. Castillo
2. Dominique Picard
3. Botond Szab'o
4. Gerard Kerkyacharian
5. Judith Rousseau

In Finance

1. Judith Rousseau
2. I. Castillo
3. Botond Szab'o
4. Dominique Picard
5. Gerard Kerkyacharian
6. Subhashis Ghosal
7. Vincent Rivoirard
8. Weining Shen

Citations in the corpus

• Thomas Bayes’ walk on manifolds (2012, background): “infinitely differentiable functions), for instance the priors considered in [31], [25].”
• On Bayesian supremum norm contraction rates (2013, methodology): “Second, strictly speaking the authors in [27] consider wavelets on the interval via periodisation, which imposes conditions at the boundary (periodic Besov spaces), conditions which can be dropped when using the CDV wavelet basis.”
• Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, methodology): “In the hierarchical setup with a prior on k, type (T1) prior has been studied by [1, 25] for generic models, by [22] for density estimation, by [2] for Gaussian white noise model and by [20] for inverse problems.”