This chapter modifies the QPLEX iterative scheme to reflect information about the counter vector observed at various time epochs and illustrates its use to perform Bayesian updates and to make prediction and dynamic adjustments. We define conditional QPLEX iterates and use them to define the joint QPLEX pmf of the counter vectors at different time epochs. We show via counterexample that the corresponding finite-dimensional joint pmfs of the counter vectors at different time epochs are not, in general, consistent. Consequently, these pmfs cannot be associated with a stochastic process (such as a Markov chain or a hidden Markov model). We use the original unconditional QPLEX iterates to define finite-dimensional joint ex-post pmfs of the counter vectors at different time epochs. These pmfs are consistent, which leads to a so-called nonlinear Markov chain of the counter vectors. However, there is a conceptual flaw underlying these ex-post pmfs.