Abstract
In this work, we study some computational aspects for the Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, the use of a latent or auxiliary random variable facilitates to obtain any posterior distribution when being related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to daily price returns of Abbey National shares, considered in [1], and the other is the length distribution analysis of coding and non-coding regions in a Homo sapiens chromosome DNA sequence, considered in [2]. Posterior summaries of interest are obtained using the OpenBUGS software.
Highlights
A wide class of distributions that encompasses the Gaussian one is given by the class of stable distributions
We study some computational aspects for the Bayesian analysis involving stable distributions
The use of stable distributions could be a good alternative for many applications in data analysis, since this model has a great flexibility for fitting the data
Summary
A wide class of distributions that encompasses the Gaussian one is given by the class of stable distributions. Considering a latent or an auxiliary variable, [1] proved a theorem that is useful to simulate samples of the joint posterior distribution for the parameters α, β, δ and σ. This theorem establishes that a stable distribution for a random variable Z defined in (−∞, ∞) is obtained as the marginal of a bivariate distribution for the random variable Z itself and an auxiliary random variable Y. The computational costs to obtain posterior summaries of interest using MCMC methods are high for this class of models, which could give some limitations for practical applications.
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