On The Gaussian Approximation To Bayesian Posterior Distributions

2020/12/01 by Christoph Fuhrmann, Hanns Ludwig Harney, Fuhrmann, Christoph +5
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2012.00748

25 pages, 2 figures

arxiv created 2020/12/01 · arxiv updated 2020/12/03

Abstract

The present article derives the minimal number N of observations needed to consider a Bayesian posterior distribution as Gaussian. Two examples are presented. Within one of them, a chi-squared distribution, the observable x as well as the parameter ξ are defined all over the real axis, in the other one, the binomial distribution, the observable x is an entire number while the parameter ξ is defined on a finite interval of the real axis. The required minimal N is high in the first case and low for the binomial model. In both cases the precise definition of the measure μ on the scale of ξ is crucial.

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