Convergence rates of posterior distributions

By Subhashis Ghosal, Jayanta Kumar Ghosh, A. van der Vaart. 2000

887 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/334b8b09488e4ef41f1bdd8e4cb3b51b01e0f226

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Citations in the corpus

BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS (2011, neutral): “26 92 v2 [ m at h. ST ] 2 3 Fe b 20 12 The Annals of Statistics 2011, Vol. 39, No. 5, 2626–2657 DOI: 10.1214/11-AOS920 c© Institute of Mathematical Statistics, 2011 BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS By B. T. Knapik1, A. W. van der Vaart and J. H. van Zanten”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “Although remarkable progress has been made in the understanding of the frequentist properties of nonparametric Bayes procedures (we refer here only to some of the key papers such as [18, 19, 34, 36, 38] and references therein), a fully satisfactory answer to the BvM-question seems not to have been f”
Dynamics of Bayesian Updating with Dependent Data and Misspecified Models (2009, background): “These contributions also make (d) certain dynamical assumptions about the data-generating process, most often that it is IID [4, 26, 65] (in this setting, [27] and [59] in particular consider convergence rates), independent non-identically distributed [13, 29], or, in some cases, Markovian [28, 29];”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, methodology): “Consistency in stronger metrics was considered by Barron, Schervish and Wasserman [1] and by Ghosal, Ghosh and Ramamoorthi [9], and, shortly after, Ghosal, Ghosh and van der Vaart [10] and Shen and Wasserman [30] developed techniques that allow us to prove frequentist rates of contraction of the pos”
Bayes procedures for adaptive inference in inverse problems for the white noise model (2012, background): “Extending the testing approach of [17,18] would be one possibility, cf.”
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors (2014, methodology): “where Φ1(α, β, γ;x, y) denotes the degenerate hypergeometric function of two variables (Gradshteyn and Ryzhik, 1965). An unanswered question so far has been how τ should be chosen. Intuitively, τ should be small if the mean vector is very sparse, as the horseshoe prior will then place more of its ma”
Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems (2012, neutral): “Following the approach in [16,10,27,9], we quantify this idea as in (1.”
Posterior concentration rates for infinite dimensional exponential families (2012, methodology): “[8], for any l, there exists a test φ(l) such that Ef0 [φ(l)] ≤ e−8Knh 2(f0,fl), sup f :h(f,fl)≤h(f0,fl)/2 Ef [1− φ(l)] ≤ e−8Knh 2(f0,fl), where K is an absolute constant.”
Rates of contraction of posterior distributions based on Gaussian process priors (2008, methodology): “1 of [8] with d equal to the L2(G)-norm.”
On adaptive posterior concentration rates (2013, background): “[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 [29]), Gaussian time series (Choudhuri et al.”
Bayesian inference with rescaled Gaussian process priors (2007, background): “It is well known that in the frequentist setup in which the data are sampled from a ﬁxed true distribution, a prior on an inﬁnite-dimensional model has to be carefully chosen in order to obtain optimal rates of contraction of the posterior (cf. e.g. [3], [17], [19], [4], [25], [23]).”
Consistency of Bernstein polynomial posteriors (2002, methodology): “To show that it is not too large, we use the following result which follows from theorem 2 of Genovese and Wasserman (2000).”
On adaptive inference and confidence bands (2011, background): “1 in [9] one could therefore heuristically conclude that the exceptional sets are “effective null-sets” from the point of view of Bayesian nonparametrics.”
BAYESIAN LINEAR REGRESSION WITH SPARSE PRIORS (2014, background): “model selection implies in particular, that the model with the largest posterior mass is model selection consistent in the frequentist sense. This can be established as in the proof of Theorem 2.5 in [22]. 2.4. Distributional approximation. In this section we show that the posterior distribution can”
Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs (2012, positive): “See, for instance, [16,14,15,36], and the references therein.”