Consistency of Bernstein polynomial posteriors

By Sonia Petrone, Larry A. Wasserman. 2002

152 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/56ed6af5bdc0724207fbe891a7f3db5d53b50a86

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Citations in the corpus

On rates of convergence for posterior distributions in infinite-dimensional models (2007, unknown): “The determination of suﬃcient conditions for Hellinger consistency has been the main goal of a number of recent papers such as, for example, [1, 2, 5] and [12].”
Bayesian Estimation of the Spectral Density of a Time Series (2004, background): “If the distribution has a continuous and bounded density, then the conclusion can be strengthened to the variation metric, and the Bernstein polynomial prior gives consistent posterior in probability density estimation (Petrone and Wasserman 2002).”
A bias-reduced approach to density estimation using Bernstein polynomials (2010, methodology): “This estimator relies on the family of the so-called Bernstein–Dirichlet priors introduced by Petrone (1999b) and has been further studied by Ghosal (2001) and Petrone and Wasserman (2002) .”
A Constructive Representation of Univariate Skewed Distributions (2006, background): “ Petrone and Wasserman, 2002 ) to model p. Given a positive integer m and a vector ! = (!1;:::;!m), a Bernstein density is given by”
Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions (2009, methodology): “Thus consistency (strong and weak) and rates of convergence can be proved using very similar techniques to those used for Bernstein polynomials (Ghosal, 2001; Petrone & Wasserman, 2002).”
Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, background): “Several papers—including [1, 2, 4, 11, 14, 15, 16, 17, 18, 20, 21, 24, 25, 26]—have been devoted to the investigation of asymptotic properties of posterior distributions on infinite-dimensional parameter spaces.”
Bayesian Survival Analysis Using Bernstein Polynomials (2005, methodology): “In particular, they have played important roles in Bayesian statistical theory (see e.g. Petrone, 1999; Petrone & Wassermann, 2002; and references therein).”
Bayesian Modelling and Inference on Mixtures of Distributions (2005, methodology): “The sum is formally infinite but for obvious practical reasons it needs to be truncated to k ≤ kn, with kn ∝ n, α < 1 (Petrone and Wasserman 2002).”
New approaches to Bayesian consistency (2004, background): “ALKER is, CN can be covered by a ﬁnite number of Hellinger balls of size δ, for any δ>0. The number of such balls will be denoted by IN(δ). More often than not, CN ⊆CN+1 and CN converges to Ω. See Petrone and Wasserman (2002), for example, who consider random densities generated via Bernstein pol”
Nonparametric Bayesian model selection and averaging (2008, methodology): “Bernstein polynomial densities with a Dirichlet prior on the mixing distribution and a geometric or Poisson prior on the order are described in Petrone [1999], Petrone and Wasserman [2002] and Ghosal [2001].”