Before revision:  We then show that, under certain conditions, 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 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.