Bayesian aspects of some nonparametric problems

By Linda H. Zhao. 2000

104 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0e4a83bad14641dcc85061ffa8134cc31daab597

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Citations in the corpus

Bayesian inverse problems with non-conjugate priors (2012, background): “[29, 34]) and, under suitable conditions on h and Πm, are adaptive over Sobolev smoothness classes in the non ill-posed case [2, 16].”
Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, methodology): “[17], van der Vaart and van Zanten [32], Zhao [35] or using a prior on λ = τ and λ = α in Belitser and Ghosal [4], Knapik et al.”
Bayes procedures for adaptive inference in inverse problems for the white noise model (2012, unknown): “2), include [33,41].”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, unknown): “r probability law given Y(n), ΠˆY n =ΠˆY (n), is also Gaussian, with mean θˆ(Y)=EΠ(θ|Y(n))=Σ(Σ+I/n)−1Y(n) =Σ(Σ+I/n)−1(y k;yℓk)t and with covariance Σ|Y(n) =Σ(nΣ+I)−1; see, for example, Theorem 3.2 in [35]. We will drop the superindex (n) from the processes Y(n) and Y(n) 0 from now on to expedite not”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, background): “Hierarchical priors, based on Gaussians but with random switches in front of the coefficients, are termed “sieve priors” in [54].”
Posterior concentration rates for infinite dimensional exponential families (2012, methodology): “The family of priors defined in Section 2 has also been used in the infinite-means model (equivalently in the white noise model) by Zhao [24] where minimax but non adaptive rates were obtained for the L2-risk (see for instance Theorem 6.1 of Zhao [24]).”
Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, unknown): “The Annals of Statistics 2006, Vol. 34, No. 6, 2897–2920 DOI: 10.1214/009053606000000911 © Institute of Mathematical Statistics, 2006”
Convergence rates of posterior distributions for non-i.i.d. observations (2007, background): “Zhao [34] and Shen and Wasserman [27] consider the case where σ 2 i,k = i−(2α+1) for i = 1, .”
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution (2003, methodology): “Zhao (2000) considered the independent normal prior with τ 2 i = τ 2 i (q) = i −(2q+1) , i = 1, 2, . . . [considered also by Cox (1993) and Freedman (1999)], and showed that the posterior mean attains the minimax rate n −q/(2q+1) .”
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”
On the Bernstein-von Mises phenomenon in the Gaussian white noise model (2011, methodology): “, [14], so that would be interesting to investigate whether the BvM statement for the squared l(2)-norm holds for sets of parameters having certain smoothness properties.”
Lower bounds for posterior rates with Gaussian process priors (2008, background): “In [17], an interesting observation about non-optimality is made, but in a rather different direction than ours, the author noting that though the prior (5) leads to the minimax rate for α = β, both the prior and the posterior put mass zero on the Sobolev space {f = (fk)k≥1, ∑ k≥1 k f(2) k < +∞} the”
Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity (2000, methodology): “By explicit computations, Zhao [23] showed that for a suitable normal prior, the posterior mean converges at the minimax rate.”
Analysis of the Gibbs Sampler for Hierarchical Inverse Problems (2013, background): “1) is an important statistical model which is known to be asymptotically equivalent to several standard statistical models, for example, nonparametric regression [9, 42].”
Nonparametric estimation of diffusions: a differential equations approach (2012, background): “An excellent reference to the white noise problem is Zhao (2000); see also Chapter 7 of Wasserman (2006) and references therein.”