What is Population stability index?

Cut a reference sample of a variable into $B$ bins (here its deciles) with shares $r_1,\dots,r_B$, and let $q_1,\dots,q_B$ be the shares of a new sample in the same bins. The population stability index is

the symmetrised Kullback–Leibler divergence between the two binned distributions (empty bins are floored at a small share).