Rast 4 is the most frequent real modulation within Bayati (if we acknowledge that the use of Nahawand 4 and Ajam 6 frequently don't feel like true modulations). It shares a tonic with Nahawand 4, and differs from Nahawand only in its raised 3rd scale degree (6th scale degree with respect to the Bayati tonic)--and hence the two are frequently paired. Sometimes Nahawand is used to "erase" the Rast and ease a re-entry into Bayati, although not always. Frequently Rast is used to reach up toward the octave tonic, as well as to Jins Bayati on the octave. And sometimes Rast simply becomes a strong alternate area of melody, offering contrast.
From "Nura Nura"
From "Samai Bayati il-3ariyan." "Husseini" refers to a suspended emphasis on 5, which eventually settles to 4. In most cases, this occurs within the context of Rast 4 (in which it could be viewed as an emphasis on 2 within Rast which settles to 1, the Rast tonic). Within Bayyati, a Husseini emphasis can also occur within Nahawand 4.
from "Taheya"
From "Ba3eed 3annak"
It is also common to find a Rast tonicization, or at least a passing emphasis, underneath the root Bayati tonic. This Rast plays more of a "supportive" role to the Bayati.
From "Nura Nura"
From "Samai Bayati il-3ariyan"
From "Taheya" dance instrumental