A0356
Title: Z-residual diagnostics for Bayesian hurdle models
Authors: Longhai Li - University of Saskatchewan (Canada) [presenting]
Abstract: Residual diagnostics is important for frequentist normal regression modelling. A fitted model's overall goodness-of-fit (GOF) is inspected by checking the residuals' normality with QQ plots and statistical tests. However, residual diagnostic tools are not available for Bayesian models. The method of Z-residual is proposed to check the adequacy of Bayesian models. The Z-residual is transformed from the cross-validatory randomized predictive p-values (RPP) with the normal quantile function. It is shown that the RPP has a uniform distribution on $(0,1)$ when the likelihood and the prior are correctly specified. Due to the uniformity of the RPPs, Z-residuals are normally distributed under the true model. Therefore, the Z-residual is used to conduct residual diagnostics for Bayesian models as for normal regression. Applying Z-residual diagnostics to Bayesian hurdle models, the graphical and numerical diagnostics are demonstrated based on Z-residuals, which can effectively identify the misspecification in the distributional family for the response variable and the misspecified covariate functional form. The sizes and powers of statistical tests are also investigated based on the Z-residual with large-scale simulation studies.
