Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution

By E. Belitser, Subhashis Ghosal. 2003

93 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/681f6e9bd5d36f86c606ebd39dd14e94ff12e40d

How researchers see this paper

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

In Artificial Intelligence

1. Kolyan Ray
2. Judith Rousseau
3. Botond Szab'o
4. I. Castillo
5. A. van der Vaart
6. Subhashis Ghosal
7. Richard Nickl
8. Johannes Schmidt-Hieber

In Environmental Engineering

1. Botond Szab'o
2. A. van der Vaart
3. Judith Rousseau
4. I. Castillo
5. Jüri Lember
6. Catia Scricciolo
7. Tzee-Ming Huang
8. Kolyan Ray

In Statistics and Probability

1. Judith Rousseau
2. Kolyan Ray
3. Botond Szab'o
4. I. Castillo
5. Richard Nickl
6. A. van der Vaart
7. Subhashis Ghosal
8. Johannes Schmidt-Hieber

Citations in the corpus

• Convergence rates for posterior distributions and adaptive estimation (2004, background): “Belitser and Ghosal (2003) dealt with adaptive estimation in the infinite normal mean set-up.”
• Bayes procedures for adaptive inference in inverse problems for the white noise model (2012, methodology): “The paper [4] follows the same approach in the direct problem.”
• Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, background): “The following construction closely follows that in [ 4 ], pages 544–545.”
• Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, methodology): “Type (T2) and (T3) priors have been studied with fixed hyper-parameters by [5, 8, 15, 33, 37] or using a prior on λ = τ and λ = α in [4, 16, 19, 30].”
• Lower bounds for posterior rates with Gaussian process priors (2008, background): “In [2], the focus is on the question of adaptation”
• Adaptive Bernstein–von Mises theorems in Gaussian white noise (2014, background): “If f0 ∈ H and α = β , it has been shown [2, 7, 27] that the posterior contracts at the minimax rate of convergence, while if α = β , then strictly suboptimal rates are achieved.”
• Nonparametric Bayesian model selection and averaging (2008, methodology): “As noted by Belitser and Ghosal [2003] suitably defined centers of these posteriors would yield adaptive point estimators.”
• On adaptive posterior concentration rates (2013, background): “These studies include in particular density estimation in the case of independent and identically distributed observations as in Ghosal et al. [16], nonparametric regression (Ghosal and van der Vaart [17]) and the white noise model (Zhao [32], Belitser and Ghosal [3]), Markov models (Tang and Ghosal”