update vignette crit

Author: Carol-seven

vignettes/crit.qmd

@@ -89,7 +89,17 @@ $$
 $$
 
 
-5. $k$-fold cross validation with negative log-likelihood loss.
+5. $K$-fold cross validation with negative log-likelihood loss.
+
+
+@fig-cv illustrates the $K$-fold cross-validation procedure used for tuning
+the parameters $\lambda$ and $\alpha$. The notation $\#\lambda$ and $\#\alpha$
+denotes the number of candidate values considered for $\lambda$ and $\alpha$,
+respectively, forming a grid of $\mathrm{\#}\lambda \times \mathrm{\#}\alpha$
+total parameter combinations. For each of the $K$ iterations, negative
+log-likelihood loss is evaluated for all parameter combinations, yielding
+$K$ performance values per combination. The optimal parameter pair is selected
+as the one achieving the lowest average loss across the $K$ iterations.
 
 
 ::: {#fig-cv}