Calculating the number of true positives from a precision-recall curve

Question

Using the below precision recall graph where recall is on x-axis and precision is on y-axis can I use this formula to calculate the number of predictions for a given precision, recall threshold ?

These calculations are based on orange trend line.

Assuming this model has been trained on 100 instances and is a binary classifier.

At recall value 0.2 there (0.2 * 100) = 20 relevant instances. At recall value 0.2 the precision = .95 so the number of true positives (20 * .95) = 19. Is this a correct method to calculate the number of true positives from precision-recall graph ?

Answer 1

Here, we should take 100 observations,a recall of 20%, and precision of 90% for making the calculations easy.

So, to produce those numbers here are two result matrices.

TP/TN->Test positive/Test Negative

CP/CN->Condition Positive/Condition Negative

        CP   CN

TP    9    1

TN    36  54

and 

          CP   CN

TP    18    2

TN    72    8

 Matrix 1:

 TP= 9

 FP = 1 and FN= 36

This results  in a recall of 9 / (36 + 9) = 20% 

and a precision of 9 / (1 + 9) = 90%

Matrix 2 

TP = 18

FP = 2 and FN = 72

This results in a recall of 18 / (72 + 18) = 20% 

and a precision of 18 / (2+18) = 90%

The graph does not give enough information to trace back the TP because two matrices with different TP and the same recall + precision can be made.

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