In the context of performance measures for classification, I have a question about recall and precision.Looking at the definition of recall:-$recall = \frac{T_p}{T_p+F_n}$When I look at this, it sounds like a $conditional$ probability to me -- probability that a test instance will be classified as positive, given that it is indeed positive:-$ recall = Pr(X\hspace{1mm}is\hspace{1mm}predicted\hspace{1mm}as\hspace{1mm}positive | X=positive ) = \frac{T_p}{T_p+F_n}$Here I am taking liberty to think (as it goes from the definition of $F_n$ ) that $F_n$ in the denominator is actually count of the test instances which are positive but got mis-classified as negative.In the same light, if I think of precision now, this is how I am thinking of it as a probabilitty that a new test instance actually being positive given that it is predicted as a positive:-$ precision = \frac{T_p}{T_p+F_p} = Pr(X=positive | X\hspace{1mm}is\hspace{1mm}predicted\hspace{1mm}as\hspace{1mm}positive)$Is this interpretation of precision and recall correct?
Interpretation of 'recall' as a conditional probability P( X=>+ | X=+ )
machine learning;classification