spacemeerkat:

Sorry for my poor understanding but if they are drawn from a multinomial does that mean that there is a random chance a sample will be drawn from a low probability region (like MCMC) or does the method stick to orderly sampling from highest to lowest probability?


There is no “random chance” but a well defined probability to draw a specific class. For example if you have a multinomial distribution with three classes A, B, and C with probabilities P(A) = 90 %, P(B) = 9 %, P(C​) = 1 %, then sampling from that distribution gives instances of class A with 90 % probability, instances of class B with 9 % proboability and instances of class C with 1 % probability.
And no. Random sampling does not define any kind of order.