114 Statistical Computing in Nuclear Imaging
which states that given the s ystem in s tate s t
he process must genera te a new
state. All of the above conditions do not imply that transition probability
P (s → s) indicating that s ystem stays in the same state s in the next move
does not have to be z ero. Interestingly if P (s → s) = 1 then the Markov
process is valid albeit trivial as the system stays in the state s. The Markov
process defined in this section will generate a succe ssion of states. When run
for a long time with properly designed transition probabilities the states that
are generated will appear in the chain with chances proportional to their prob-
abilities and ther efore will be the samples from the pr obability measure p(s).
Another ...