(2006-11) Cancho, Vicente Garibay; Aoki, Reiko; Lachos, Victor H.

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The skew-normal distribution is a class of distributions which includes the normal
distributions as a special case. In this paper, we explore the use of Markov Chain Monte
Carlo (MCMC) methods to develop a Bayesian analysis in multivariate null intercept
measurement error model (Aoki et al., 2003b) where the unobserved value of the covariate (latent variable) follows a skew—normal distribution. The results and methods are applied to a real dental clinical trial presented in Hadgu and Koch (1999).

(2006-02) Cancho, Vicente Garibay; Ortega, Edwin. M.; Lachos, Victor H.

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In this paper we discussed inference aspects of the skew-normal calibration comparative models (SN-CCM) following both; a classical and Bayesian approach, extending the usual normal calibration comparative models (N-CCM) in order to avoid data transformation. To the proposed model we consider the maximum likelihood approach to estimation via the EM-algorithm and derive the observed information matrix allowing direct inference implementation, then we conduct the Bayesian approach via Markov chain Monte Carlo procedure. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al (2003) which has a shape parameter that defines the direction of the asymmetric of the distribution, usually called the skew-ness parameter. Sahu’s skew-normal distribution is attractive because estimation of the skewness parameter does not present the same difficult as is the case with Azzalini’s (1985) one the procedures are illustrated with a numerical example.