QA264 : Approximating posterior distributions by using Edgeworth expansion and Stein’s Identity
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2014
Authors:
Abstarct: In many applications, researchers are interested to approximate a probability distribution
function. The Edgeworth expansion is a method for this aim. The Edgeworth
expansion is a series that approximates a probability distribution in terms of its cumulants.
One can derive it by first expanding the probability distribution in Hermite
orthogonal functions and then collecting terms in powers of the sample size. In this
thesis, by using a version of Stein’s Identity and properties of Hermite polynomials,
we derive an expansion for posterior distributions which possesses these features of
an Edgeworth series. Then, we compare the performance of the proposed series with
the previous ones from a Bayesian perspective. Finally, two examples are provided to
illustrate the accuracy of the proposed expansion.
Keywords:
#Edgeworth expansion #Hermite polynomials #posterior distribution #Stein’s Identity. Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: