On rates of convergence for posterior distributions in infinite-dimensional models

By Stephen G. Walker, Antonio Lijoi, Igor Prünster. 2007

85 citations recorded by the source corpus.

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. Crucially, no sieve or entropy measures are required and so rates do not depend on the rate of convergence of the corresponding sieve maximum likelihood estimator. In particular, we improve on current rates for mixture models.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c96dc63e65de4f55b8898f54d0622310aadeece5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Dirichlet Process Mixtures of Generalized Linear Models (2009, methodology): “In this case, we can specify a conjugate base measure component by component: The Gibbs sampler can still be collapsed, but the computational cost is much lower than the full Normal-Inverse-Wishart.”
Bayesian inference with rescaled Gaussian process priors (2007, background): “It is well known that in the frequentist setup in which the data are sampled from a fixed true distribution, a prior on an infinite-dimensional model has to be carefully chosen in order to obtain optimal rates of contraction of the posterior (cf. e.g. [3], [17], [19], [4], [25], [ 23 ]).”
On posterior contraction of parameters and interpretability in Bayesian mixture modeling (2019, background): “See, for instance, [14, 17, 46] for theoretical results specifically on DP mixtures, and [15, 47, 52] for general BNP models.”
Posterior Concentration for Sparse Deep Learning (2018, methodology): “Proving techniques for statements of type (10) were established in several pioneering works including Ghosal, Ghosh and van der Vaart (2000), Ghosal and van der Vaart (2007), Shen and Wassermann (2001), Wong and Shen (1995), Walker et al. (2007).”