diff --git a/doc/BookChapters/chapter4.do.txt b/doc/BookChapters/chapter4.do.txt
index 50c719220..4bf3929dc 100644
--- a/doc/BookChapters/chapter4.do.txt
+++ b/doc/BookChapters/chapter4.do.txt
@@ -566,8 +566,20 @@ features are of relevance and which are not. This leads  us to
 the classical Principal Component Analysis (PCA) theorem with
 applications. This will be discussed later this semester ("week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html").
 
+Here we present a further way to present our results in terms of a so-called _confusion matrix_, the cumulative gain and the _ROC_ curve.
+This way of displaying our data are based upon different ways to classify our possible outcomes. Before we proceed we need some definitions.
+o _TP_: true positive or in other words, something equivalent with a proper classification
+o _TN_: true negative, which is equivalent with a correct rejection
+o _FP_: false positive, or in simpler words something that is equivalent with a false alarm
+o _FN_: false negative, which is mean to be equivalent with a miss.
 
-
+The total data set is then the sum of the true positive and true negative targets or outputs, labeled by $n$.
+Based on this we can then define the accuracy score as the sum of correctly predicted _TP_ and _TN_ cases divided by the sum of true positive and treue negative events in our data set, or as
+!bt
+\[
+\mathrm{Accuracy} = \frac{\sum_{i=0}^{n-1}I(y_i=\tilde{y}_i)}{n}.
+\]
+!et
 
 !bc pycod 
 import matplotlib.pyplot as plt