1. A method to generate random sequences based on a stochastic generative model having multiple random variates, the method implemented by one or more computer programs executed by one or more processors such that execution of the computer programs by the processors causes performance of the method, the method comprising: receiving a plurality of inputs representative of the stochastic generative model, the inputs comprising: a first random variate having a finite set of alphabets; a second random variate having a set of alphabets; and, a third random variate having a finite set of alphabets; generating a plurality of outputs representative of the random sequences based on the stochastic generative model, by the processors executing the computer programs, the outputs comprising: a first random sequence, the first random sequence being a finite-length random sequence of alphabets randomly selected from the first random variate; a second random sequence having a set of alphabets selected from the second random variate, the set of alphabets of the second random sequence corresponding to each alphabet of the first random sequence; and, a third random sequence having a set of alphabets randomly selected from the third random variate, the set of alphabets of the third random sequence corresponding to each alphabet in the first random sequence.