Ah yes, read channels for disk drives, now applicable to SerDes.
PRML = Partial Response
and Maximum Likelihood.
They are two separate things to understand.
Partial response is all about low pass filtering such that the higher frequency harmonics are removed and a better SNR and better BER are the result.
However, Partial Response means with higher harmonics removed the signal will have some "ringing" because the higher frequencies have been removed.
If you sample the signal at the null points of the ringing the signal sampled still represents the original signal.
Those samples can be used to represent the signal in a time domain sampled system, where the samples are compared to the expected ideal sampled signal. The difference between observed and expected are recorded and used to make a decision with respect to what was the actual signal. A Viterbi detector is used to do the math for this.
Best short form explanation I can toss out there.
BTW, back when PRML was a new thing to disk drives (circa 1992) some people used to call it:
PRML = Partially Right Mostly Lucky!