I am running a logisitc regression and trying to interpret the predictive power it generates. How should I interpret the precision/recall curve and the accuracy as a function of threshold?
My precision/recall curve looks very strange with the immediate dip.
At the left end of your precision/recall curve, you classify everything as "negative". So you have $TP=FP=0$. No matter how many true positives $P$ you have (assuming $P>0$), your recall is
$$ \frac{TP}{P}=\frac{0}{P}=0. $$
On the other hand, your precision is
$$ \frac{TP}{TP+FP}=\frac{0}{0+0}=\frac{0}{0}, $$
which is undefined, but your software may simply set it to (or plot it as) one.
Very much related: Why is accuracy not the best measure for assessing classification models? and Classification probability threshold. So, in reply to your question "How should I interpret the precision/recall curve and the accuracy as a function of threshold?", my answer would be "don't".
