On Bayesian consistency

By Stephen G. Walker, Nils Lid Hjort. 2001

129 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c9c4160f8696e265f3ea0a25fba872f4fafd2a6e

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Citations in the corpus

Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, methodology): “Preliminary ascertainment of consistency is based on results by Barron, Schervish and Wasserman [2], Walker and Hjort [23] and Walker [22], who have addressed the issue of consistency of posterior distributions for infinitedimensional exponential families generated by orthonormal systems of bounded ”
Bayesian fractional posteriors (2016, background): “While [59] established consistency of power posteriors for well-specified models; see also [43] for certain rate results; we derive rates of convergence for the fractional posterior for general non-i.”
Approximate Models and Robust Decisions (2014, methodology): “For example, models involving composite likelihoods, integrated nested Laplace approximations (INLA), Variational Bayes, Approximate Bayesian Computation (ABC), all start with the premise of misspecification; see, for example, Beaumont, Zhang and Balding (2002), Fearnhead and Prangle (2012), Marjora”
Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector (2013, methodology): “As in Walker and Hjort (2001), this fractional likelihood posterior is a powerful tool, though our concentration results do not follow immediately from theirs.”
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It (2014, methodology): “The definition of η-generalized posterior now specializes to the definition of ‘generalized posterior’ (in this context also called “fractional posterior”) as known within the Bayesian literature (Walker and Hjort, 2002; Zhang, 2006a; Martin et al., 2017):”
On the use of non‐local prior densities in Bayesian hypothesis tests (2010, background): “null hypothesis (as well as other null hypotheses defined with respect to non-local priors) decreases at a rate that is linear in n (e.g., Bahadur and Bickel, 1967; Walker and Hjort, 2001; Walker, 2004).”
A Bayesian approach to non‐parametric monotone function estimation (2009, methodology): “This technique, of using a combination of the consistency of the maximum likelihood estimator and a Bayesian component, was first introduced in Walker and Hjort (2001) and is applicable whenever the maximum likelihood estimator exists, which it does in isotonic regression.”
Assigning a value to a power likelihood in a general Bayesian model (2017, background): “See, for example, Royall & Tsou (2003), Zhang (2006a), Zhang (2006b), Jiang & Tanner (2008), Bissiri, Holmes & Walker (2016), Walker & Hjort (2001), Watson & Holmes (2016), Miller & Dunson (2015), Grünwald & van Ommen (2014), Syring & Martin (2015), and more generally Hansen & Sargent (2008).”
From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation (2006, background): “∀ γ > 0, we deﬁne a generalized Bayesian posterior π γ ( ·| X ) with respect to π as (also see (Walker & Hjort, 2001)): We call π γ the γ -Bayesian posterior.”