In Example 3.1, adapt the code to include a posterior predictive (p)-tests to assess skewness and kurtosis

Question:

In Example 3.1, adapt the code to include a posterior predictive $p$-tests to assess skewness and kurtosis in the residuals. For example, the $p$-test for skewness would compare a skew measure for replicates

Data from Example 3.1

\[D_{\text {rep }}^{\text {skew }}=\frac{1}{n} \sum_{i=1}^{n} \varepsilon_{\text {rep }, i}^{3(t)} / \sigma^{3(t)} \quad \text { against } \quad D_{\text {obs }}^{\text {skew }}=\frac{1}{n} \sum_{i=1}^{n} \varepsilon_{i}^{3(t)} / \sigma^{3(t)}\]