An automatic method for generating random variates with a given characteristic function
SIAM Journal on Applied Mathematics
Approximation of multidimensional stable densities
Journal of Multivariate Analysis
Signal processing with alpha-stable distributions and applications
Signal processing with alpha-stable distributions and applications
Numerical approximation of the symmetric stable distribution and density
A practical guide to heavy tails
Bayesian inference for α-stable distributions: A random walk MCMC approach
Computational Statistics & Data Analysis
Inference in symmetric alpha-stable noise using MCMC and the slice sampler
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 06
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
On-line Bayesian estimation of signals in symmetric α-stable noise
IEEE Transactions on Signal Processing
Estimation of stable spectral measures
Mathematical and Computer Modelling: An International Journal
Likelihood-free Bayesian estimation of multivariate quantile distributions
Computational Statistics & Data Analysis
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@a-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 @a-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, @a-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 @a-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.