Unlike the general form in Eq. 5, the forward model Y (x t ) = h • r(S) represents only the single-step reaction model r(S), and consequently the auxiliary distribution π t (x t ) is a function of two reactants only. Nevertheless, the model is able to represent general reaction networks by selecting the already calculated intermediate products contained in B t , to which their reaction networks are implicitly assigned. Specifically, we proceed with the following SMC procedure. In step t -1, a sample set {x i t-1 |i = 1, . . . , m} of reactant set x t-1 is obtained, and a new set {x i t |i = 1, . . . , m} is generated using the proposal η(x t |x t-1 ), where each x t is sampled from B t . Here, all newly generated products P i = r(x i t ) (i = 1, . . . , m) are added to the set of candidate reactants in the next step, as follows: