Abstract
The scale mixtures of Normal distributions are used as a robust alternative to the normal distribution in linear regression modelling, and a non-iterative Bayesian sampling algorithm is developed to obtain independently and identically distributed samples approximately from the observed posterior distributions, which eliminates the convergence problems in iterative Gibbs sampling. Model selection and influential analysis are conducted to choose the best fitted model and to detect the latent outliers. The performances of the methodologies are illustrated through several simulation studies by comparison with the Normal regression and Gibbs sampling, and finally, the US treasury bond prices data is analyzed using the proposed algorithm.
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