Second, the verb w would be passed through a communication "channel" and be corrupted by the "noise" to produce the percentage change x according to the likelihood function (aka the channel model) P (x|w).
the percentage change x that we see is actually the distorted form of its associated verb w. An alternative, but equivalent, interpretation is that when a pair (x, w) is passed through the noisychannel, the verb w will be lost and finally only the percentage change x will be seen.