Noname manuscript No. (will be inserted by the editor) A semiparametric Bernstein- von Mises theorem for Gaussian process priors

Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, background): “These values can be upper bounded under usual smoothness conditions on f , e.g. if f belongs to a Sobolev ball with a certain regularity; cf. Bontemps (2011); Bickel and Kleijn (2012); Castillo (2012).”
A Bernstein–von Mises theorem for smooth functionals in semiparametric models (2013, methodology): “In [10], a slightly weaker version of condition (2.”
Adaptive Bernstein–von Mises theorems in Gaussian white noise (2014, background): “Bickel and Kleijn [3], Castillo [8], Rivoirard and Rousseau [41] and Castillo and Rousseau [13] provide sufficient conditions for BvMs for semiparametric functionals.”
The semiparametric Bernstein-von Mises theorem (2010, background): “Castillo [6] considers marginal posteriors in Cox’s proportional hazards model and Stein’s symmetric location problem from a unified point of view.”
Large ball probabilities, Gaussian comparison and anti-concentration (2017, background): “o, it suﬃces to compare two probabilities IP a+ξ ≤ r vs IP ξ G ≤ r for all r≥ 0. Existing results cover only very special cases; see e.g. Johnstone (2010); Bontemps (2011); Panov and Spokoiny (2015); Castillo (2012); Castillo and Nickl (2013); Belitser (2017) and references therein. Most of the ment”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, methodology): “I. Castillo would like to thank the Cambridge Statistical Laboratory as well as Queens’ College Cambridge for their hospitality during his visit to Cambridge, where parts of this research were carried out.”
On the Frequentist Properties of Bayesian Nonparametric Methods (2016, background): “In (Castillo, 2010) and (Bickel and Kleijn, 2012) sufficient conditions are proposed to derive BvM in separated models in the form θ = (ψ, η).”
Bernstein - von Mises Theorem for growing parameter dimension (2013, background): “…for high dimensional linear models; Boucheron and Gassiat (2009), Kim (2006) for non-Gaussian models; Shen (2002), Bickel and Kleijn (2012), and Castillo (2012) for the semiparametric version of the BvM result; Kleijn and van der Vaart (2006), Bunke and Milhaud (1998), for the misspecified…”
On Bayesian supremum norm contraction rates (2013, methodology): “[4], [5], [7], equal to √ n〈f − f0, ζl,k −Al,k〉2 = √ n ˆ 1”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, background): “[7]).”
BERNSTEIN-VON MISES THEOREM FOR LINEAR FUNCTIONALS OF THE DENSITY (2009, background): “Other differences with our paper have to be pointed out: The centering considered by [21] is based on the sieve maximum likelihood estimate, whereas priors considered by [3] are merely Gaussian in the information loss case.”