Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity

By Subhashis Ghosal. 2000

75 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, background): “We mention Ghosal (1999, 2000), Boucheron and Gassiat (2009), Johnstone (2010) and Bontemps (2011) for specific examples.”
Noname manuscript No. (will be inserted by the editor) A semiparametric Bernstein- von Mises theorem for Gaussian process priors (unknown): “However, positive BVM results are known in particular nonparametric settings, see [10,17].”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, background): “In [15] it is shown that the dimensionality constraint can be relaxed to pn/n → 0 for exponential models with a product structure.”
BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS (2011, unknown): “26 92 v2 [ m at h. ST ] 2 3 Fe b 20 12 The Annals of Statistics 2011, Vol. 39, No. 5, 2626–2657 DOI: 10.1214/11-AOS920 c© Institute of Mathematical Statistics, 2011 BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS By B. T. Knapik1, A. W. van der Vaart and J. H. van Zanten”
A Bernstein-Von Mises Theorem for discrete probability distributions (2008, methodology): “, 2001; Fan, 1993) and in the context of Bayesian inference (Ghosal, 2000).”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “A number of BvM-type results have been obtained for the fixed finite-dimensional posterior with dimension increasing to infinity: Ghosal [16] and Bontemps [6] consider regression with a finite number of regressors, Ghosal [17] and Clarke and Ghosal [9] consider exponential families, and the case of ”
Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors (2010, background): “In particular two situations have been studied: regression models in [7]; exponential models in [8], [4], and [2] (this last one deals with the discrete case, when the observations follow some unknown infinite multinomial distribution).”
High dimensional Bernstein-von Mises: simple examples (2010, background): “Ghosal [7, 8, 9] developed posterior normality results for the full posterior in cases where the dimension of the parameter space increases sufficiently slowly.”