update

doc/src/week45/week45.do.txt

@@ -329,21 +329,38 @@ o The true negative $TN$ number which represents whether a negative test has bee
 o The false positive $FP$ number, a so-called type I error which tells us about the fraction of  positive test result which are wrongly classified
 o A false negative $FN$ number, a so-called type II error which, should be pretty obvious, indicates if a negative test has been wrongly classified.
 
+It is is easy to think in terms of illness. You could think of the above as
+o True positive: Sick people correctly identified as sick
+o False positive: Healthy people incorrectly identified as sick
+o True negative: Healthy people correctly identified as healthy
+o False negative: Sick people incorrectly identified as healthy
 
 !split
 ===== Combinations of classification results =====
 
 It is common in the literature to define various combinations the above numbers. The most commonly used are
 
-!bblock Sensitivity, recall, hit rate, or true positive rate $TPR$
+!bblock Sensitivity, recall, hit rate, or true positive rate $TPR$. It is the probability of a positive test result, conditioned on the individual truly being positive.
 !bt
 \[
 {\displaystyle \mathrm {TPR} ={\frac {\mathrm {TP} }{\mathrm {P} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}=1-\mathrm {FNR} }
 \]
 !et
 !eblock
+The $TPR$ defines how many correct positive results occur among all positive samples available during the test
 
-!bblock Specificity, selectivity or true negative rate $TNR$
+
+!bblock Miss rate or false negative rate $FNR$
+!bt
+\[
+{\displaystyle \mathrm {FNR} ={\frac {\mathrm {FN} }{\mathrm {P} }}={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TP} }} }
+\]
+!et
+!eblock
+
+
+
+!bblock Specificity, selectivity or true negative rate $TNR$. It is the probability of a negative test result, conditioned on the individual truly being negative.
 !bt
 \[
 {\displaystyle \mathrm {TNR} ={\frac {\mathrm {TN} }{\mathrm {N} }}={\frac {\mathrm {TN} }{\mathrm {TN} +\mathrm {FP} }}=1-\mathrm {FPR} }
@@ -356,8 +373,21 @@ with the fall-out false positive rate
 \]
 !et
 !eblock
+The $FPR$ defines how many incorrect positive results occur among
+all negative samples available during the test.
 
-!bblock Precision or positive predictive value $PPV$
+!split
+===== Positive and negative prediction values =====
+
+The positive and negative predictive values 
+are the proportions of positive and negative results in statistics and
+diagnostic tests that are true positive and true negative results,
+respectively.[1] The PPV and NPV describe the performance of a
+diagnostic test or other statistical measure. A high result can be
+interpreted as indicating the accuracy of such a statistic.
+
+
+!bblock Precision or positive predictive value $PPV$. 
 !bt
 \[
 {\displaystyle \mathrm {PPV} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FP} }}=1-\mathrm {FDR} }
@@ -374,13 +404,9 @@ with the fall-out false positive rate
 !eblock
 
 
-!bblock Miss rate or false negative rate $FNR$
-!bt
-\[
-{\displaystyle \mathrm {FNR} ={\frac {\mathrm {FN} }{\mathrm {P} }}={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TP} }} }
-\]
-!et
-!eblock
+!split
+===== Other quantities =====
+
 
 
 !bblock False discovery rate $FDR$
@@ -434,10 +460,17 @@ graphical plot that illustrates the performance of a binary classifier
 model at varying threshold values.
 
 The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting.
+
+To draw a ROC curve, only the true positive rate (TPR) and false
+positive rate (FPR) are needed (as functions of some classifier
+parameter). The TPR defines how many correct positive results occur
+among all positive samples available during the test. FPR, on the
+other hand, defines how many incorrect positive results occur among
+all negative samples available during the test.
+
+
 See URL:"https://en.wikipedia.org/wiki/Receiver_operating_characteristic" for more discussions.
 
-
-
 !split
 ===== Cumulative gain curve =====
 
@@ -447,7 +480,7 @@ fraction of examples correctly classified
 against Predictive Positive Rate, which represents 
 the fraction of positively predicted examples.
 
-
+The examples below show the confusion matrix, the ROC curve and the cumulative gain for the Wisconsin cancer data.
 
 
 !split