for t in 1...T:
    new_a = ... //propose new variables a
    p = min(1,p(X|new_a,b)/p(X|a,b))
    thresh  = ... //a random number generated from a uniform [0,1]
    if thresh < p:
       a = new_a //accept new_a
    new_b = ... //propose new variables b
    p = min(1,p(X|a,new_b)/p(X|a,b))
    thresh  = ... //a random number generated from a uniform [0,1]
    if thresh < p:
       b = new_b //accept new_b

for t in 1...T:
    new_a = ... //propose new variables a
    new_b = ... //propose new variables b
    p = min(1,p(X|new_a,new_b)/p(X|a,b))
    thresh  = ... //a random number generated from a uniform [0,1]
    if thresh < p:
       a = new_a, b = new_b //accept both a and b