Likelihood-Free Bayesian Inference for α-Stable Models

33 Pages Posted: 10 Jun 2017

See all articles by Gareth Peters

Gareth Peters

University of California Santa Barbara; affiliation not provided to SSRN

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: December 23, 2009

Abstract

α-stable distributions are utilized as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate αα-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, αα-stable models are practically limited to the univariate setting under the Bayesian paradigm, and to bivariate models under the classical framework. A novel Bayesian approach to modelling univariate and multivariate α-stable distributions is introduced, based on recent advances in “likelihood-free” inference. The performance of this procedure is evaluated in 1, 2 and 3 dimensions, and through an analysis of real daily currency exchange rate data. The proposed approach provides a feasible inferential methodology at a moderate computational cost.

Keywords: α-stable distributions; Approximate Bayesian computation; Bayesian inference; Likelihood-free inference; Multivariate models

Suggested Citation

Peters, Gareth and Sisson, Scott and Fan, Y., Likelihood-Free Bayesian Inference for α-Stable Models (December 23, 2009). Available at SSRN: https://ssrn.com/abstract=2980440 or http://dx.doi.org/10.2139/ssrn.2980440

Gareth Peters (Contact Author)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

affiliation not provided to SSRN

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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