Pseudo-Marginal MCMC for Parameter Estimation in alpha-Stable Distributions

The alpha-stable distribution is very useful for modelling data with extrelne values and skewed behaviour. The distribution is governed by two key parameters, tail thickness and skewness, in addition to scale and location. Inferring these parameters is difficult due to the lack of a closed form expression of the probability density. We develop a Bayesian method, based on the pseudo-marginal MCMC approach, that requires only unbiased estimates of the intractable likelihood. To compute these estimates we build an adaptive importance sampler for a latent variable-representation of the alpha-stable density. This representation has previously been used in the literature for conditional MCMC sampling of the parameters, and we compare our method with this approach. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.