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In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.
Respiratory diseases and air pollution
are the goals of many scientific works, but studies of the relations between
these diseases and cane field burning pollution are still not well studied in the
literature. In this work, we consider the times between days of extrapolations of the number of
daily hospitalizations due to respiratory diseases as our data. To analyze this
data set, we introduce different statistical models related to burning focus
pollution and their relations with the counting of hospitalizations due to
respiratory diseases. Under a Bayesian approach and with the help of the free
available WinBUGS software, we get posterior summaries of interest using
standard MCMC (Markov Chain Monte Carlo) methods.