Pseudo-Marginal MCMC for Parameter Estimation in α-Stable Distributions**The first author acknowledges partial funding from EPSRC-DTG- 2013/EU, while the second and third authors were supported by the EPSRC BTaRoT project EP/K020153/1; the third author was also funded by the Learning of complex dynamical systems project (Contract number: 637-2014-466) from the Swedish Research Council.
Marina Riabiz, Fredrik Lindsten, Simon Godsill · IFAC-PapersOnLine · 2015
The α-stable distribution is very useful for modelling data with extreme 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 latentvariable- representation of the α-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.