The goal of SMC is to efficiently approximate the entire system π A (x) with the Monte Carlo approximator, successively sampling x t in the order t = 0, 1, . . . , T . The definition of the auxiliary distribution is arbitrary. For example, if the last auxiliary distribution is defined as the original target π T (x T ) = π(x), we can take a sample set of x T to obtain an approximate distribution. Alternatively, all T auxiliary distributions π 1 (x 1 ) . . . , π T (x T ) can be set to be identical to the target π(x). In this case, all samples of x 1 , . . . , x T can be used for the approximate inference. The essence of SMC methodology is to be able to use any sequence of auxiliary distributions to efficiently obtain random samples from the intractable target distribution.