Before revision:  We then show, under time-scale separation and other assumptions, that this log-likelihood  can be approximately computed by using the continuous-time signals of the number of active TF molecules and the number of bound promoters when the input is persistent.
After revision:  We then show, under time-scale separation and other assumptions, that this log-likelihood ratio can be approximately computed by using the continuous-time signals of the number of active TF molecules and the number of bound promoters when the input is persistent.