Likelihood-free Bayesian inference for α-stable models

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 α-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, α-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.