Mixed Poisson regression models with Gaussian latent variables are asymptotically robust to infinite target values but not to infinite covariate values, as shown for Poisson-Gamma, Poisson-log-t, and Poisson-RSB targets.
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On Asymptotic Outlier Rejection in Bayesian Mixed Poisson Regression Models Under Extreme Target and Covariate Values
Mixed Poisson regression models with Gaussian latent variables are asymptotically robust to infinite target values but not to infinite covariate values, as shown for Poisson-Gamma, Poisson-log-t, and Poisson-RSB targets.