Convergence rates for posterior distributions and adaptive estimation

By Tzee-Ming Huang. 2004

71 citations recorded by the source corpus.

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.

View Paper: https://www.semanticscholar.org/paper/5400b7229d393016d8ef51aee1b4f559c2abc79a

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Citations in the corpus

Posterior concentration rates for infinite dimensional exponential families (2012, methodology): “Also related to adaptation are the works of Huang [11] and Ghosal et al. [9] who derive a general framework to obtain adaptive posterior concentration rates, the former applies her results to the Haar basis case.”
Adaptive Bayesian Procedures Using Random Series Priors (2014, methodology): “We apply the method on two interesting data sets on functional regression.”
Bayesian inverse problems with non-conjugate priors (2012, background): “[11, 13, 16, 29, 31] for some examples), but the situation of inverse problems has only recently been considered and then only in the conjugate setting [1, 20, 21], where explicit posterior expressions are available.”
Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, methodology): “In a recent paper, Huang [16] has obtained results on posterior rates of convergence for density estimation using the method of exponentials, with priors on the coefficients of the log-density expansion via wavelets, the coefficients lying in a Besov space B 2,2 with α ∈ (0,1).”
Adaptive Bayesian density estimation with location-scale mixtures (2010, background): “The problem of ﬁnding general conditions for statistical models under which (3) holds has been studied in among others [11], [13], [32], [17], [8] and [29].”
BERNSTEIN-VON MISES THEOREM FOR LINEAR FUNCTIONALS OF THE DENSITY (2009, methodology): “For the wavelet case, [13] considered the special case of the Haar basis.”
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution (2003, methodology): “The inference based on such a prior is therefore adaptive in the sense that the same prior gives the optimal rate of convergence irrespective of the smoothness condition. Here, besides the problem of estimation, we encounter the problem of model selection. In a Bayesian framework, perhaps the most n”