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Francisco J. Rubio Alvarez 《Revue internationale de statistique》2020,88(3):793-796
We show that the family of asymmetric distributions studied in a recent publication in the International Statistical Review is equivalent to the family of two-piece distributions. Moreover, we show that the location-scale asymmetric family proposed in that publication is non-identifiable (overparameterised), and it coincides with the family of two-piece distributions after removing the redundant parameters. 相似文献
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Scattered reports of multiple maxima in posterior distributions or likelihoods for mixed linear models appear throughout the literature. Less scrutinised is the restricted likelihood, which is the posterior distribution for a specific prior distribution. This paper surveys existing literature and proposes a unifying framework for understanding multiple maxima. For those problems with covariance structures that are diagonalisable in a specific sense, the restricted likelihood can be viewed as a generalised linear model with gamma errors, identity link and a prior distribution on the error variance. The generalised linear model portion of the restricted likelihood can be made to conflict with the portion of the restricted likelihood that functions like a prior distribution on the error variance, giving two local maxima in the restricted likelihood. Applying in addition an explicit conjugate prior distribution to variance parameters permits a second local maximum in the marginal posterior distribution even if the likelihood contribution has a single maximum. Moreover, reparameterisation from variance to precision can change the posterior modality; the converse also is true. Modellers should beware of these potential pitfalls when selecting prior distributions or using peak‐finding algorithms to estimate parameters. 相似文献
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