An Analysis of Bayesian Inference for Nonparametric Regression

By Dennis D. Cox. 1993

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, methodology): “s one often faces very complicated models involving a lot of parameters and with a limited sample size. This requires an extension of the classical results to such non-classical situation. We mention Cox (1993); Freedman (1999); Ghosal (1999); Johnstone (2010) and references therein for some special”
Asymptotic Normality of Semiparametric and Nonparametric Posterior Distributions (2002, methodology): “A critical assumption here is that p=d is larger than 1=2, which ensures that ˜—n D o4nƒ1=25 in (8) and hence eliminates the phenomenon of Cox (1993).”
On the Frequentist Properties of Bayesian Nonparametric Methods (2016, background): “Cox, 1993.”
Frequentist coverage and sup-norm convergence rate in Gaussian process regression (2017, background): “…(BvM) theorem under the total variation metric holds fairly generally and guarantees asymptotically nominal coverage of Bayesian credible intervals, the story of the frequentist validity of credible intervals/bands in inﬁnite dimensional models is more complicated and delicate [16, 20, 24, 27].”
Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression (2014, background): “Since optimal smoothing typically makes the order of the bias and variability the same, credible region may lack adequate coverage, see [4, 7] for the Gaussian white noise model.”
High dimensional Bernstein-von Mises: simple examples (2010, methodology): “In this section, we pay homage to a remarkable paper by Freedman [6], itself stimulated by Cox [4], which sets out the failure of the Bernstein-von Mises theorem in a simple sequence model of function estimation in Gaussian white noise.”
The semiparametric Bernstein-von Mises theorem (2010, background): “ Hk[0;1]. The necessity of a penalty in the ML procedure signals that the choice of a prior H for the nuisance is a critical one. Indeed, it has been shown in a related regression model by Cox (1993) [12] that the Bernstein-Von Mises limit does not occur if one makes the wrong choice for the nuisanc”
Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, methodology): “estimation, by Babenko and Belitser [2] for Gaussian white noise model and by Ray [23] for inverse problems. Type (T2) and (T3) priors have been studied with ﬁxed hyperparameters by Castillo [6], Cox [8], Knapik et al. [17], van der Vaart and van Zanten [32], Zhao [35] or using a prior on λ= τand λ=”
The Bernstein–von Mises theorem for the proportional hazard model (2006, background): “This unfortunate phenomenon continues to occur in the posterior convergence rate. See [ 2 , 9, 23, 25].”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “Cox [11] and Freedman [14] have shown the impossibility of a nonparametric BvM result in a strict L2-setting.”
A Bernstein–von Mises theorem in the nonparametric right-censoring model (2004, background): “Cox (1993) and Zhao (2000) showed that this unfortunate phenomenon continues to occur in the posterior convergence rate.”
BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS (2011, methodology): “The model considered in [7] is equivalent to our model (1.”
Philosophy and the practice of Bayesian statistics (2010, unknown): “At a more philosophical level, the idea that a central task of statistical analysis is the search for specific, consequential errors has been forcefully advocated by Mayo (1996), Mayo and Cox (2006); Mayo and Spanos (2004), and Mayo and Spanos (2006). Mayo has placed a special emphasis on the idea o”
A Bayesian approach to non‐parametric monotone function estimation (2009, background): “However, the statistical literature (e.g. Freedman (1999) and Cox (1993)) has provided numerous surprises and anomalies when the number of parameters is infinite.”
Simultaneous Confidence Bands for Penalized Spline Estimators (2010, methodology): “This agrees with the findings of Cox (1993).”
Non-Gaussian statistical inverse problems. Part I: Posterior distributions (2012, methodology): “It was later adopted to describing infinite-dimensional unknowns (see for example [24]), but its main application has been in providing finite-dimensional approximations of Gaussian random variables.”
On the Bernstein-von Mises phenomenon in the Gaussian white noise model (2011, background): “, [1, 11, 12] for semiparamatric and [5, 6] for nonparametric, the results in [2] and [3] led to the widely accepted belief that the BvM phenomenon does not occur in the nonparametric framework.”