Likelihood-free Bayesian inference for -stable models
- 作者：G.W. Peters GarethPeters@unsw.edu.au ; S.A. Sisson ; scott.sisson@unsw.edu.au ; Y. Fan
- 关键词：伪-stable distributions ; Approximate Bayesian computation ; Bayesian inference ; Likelihood-free inference ; Multivariate models
- 刊名：Computational Statistics and Data Analysis
- 出版年：2012
- 期刊代码：19_01679473
- 类别：cp
- 出版时间：November, 2012
- 卷：56
- 期：11
- 页码：3743-3756
- 文件大小：626 K
摘要
-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 -stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, -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 -stable distributions is introduced, based on recent advances in 鈥渓ikelihood-free鈥?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.