Bayesian inference for αα-stable distributions: A random walk MCMC approach

A novel approach for Bayesian inference in the setting of αα-stable distributions is introduced. The proposed approach resorts to a FFT of the characteristic function in order to approximate the likelihood function. The posterior distributions of the parameters are then produced via a random walk MCMC method. Contrary to the existing MCMC schemes, the proposed approach does not require auxiliary variables, and so it is less computationally expensive, especially when large sample sizes are involved. A simulation exercise highlights the empirical properties of the sampler. An application on audio noise data demonstrates how this estimation scheme performs in practical applications.